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17Calculus Precalculus - Exponent Rules

17Calculus
Single Variable Calculus
Derivatives
Integrals
Multi-Variable Calculus
Precalculus
Functions

In calculus you will be required to understand and be able to use the rules of exponents. Most instructors will not go over these rules before jumping into calculus. So make sure you know them well.

List of Rules

Let's start by going through these exponent rules.

1. The Product Rule

\( x^n \cdot x^m = x^{n+m} \)

2. The Quotient Rule

\(\displaystyle{ \frac{x^n}{x^m} = x^{n-m} }\)

3. The Power Rule

\( (x^n)^m = x^{n \cdot m} \)

4. Power of Zero

\( x^0 = 1 \)

5. Negative Exponents

\(\displaystyle{ x^{-n} = \frac{1}{x^n} }\)

6. Fractional Exponents

\( x^{1/n} = \sqrt[n]{x} \)

7. Distribute An Exponent Over a Product

\( (x \cdot y)^n = x^n y^n \)

8. Distribute An Exponent Over a Quotient

\(\displaystyle{ \left( \frac{x}{y} \right)^n = \frac{x^n}{y^n} }\)

In this video clip, the instructor explains these rules very well and includes some examples.

freeCodeCamp.org - College Algebra - Exponent Rules [10mins-13secs]

video by freeCodeCamp.org

This instructor also does a great job explaining these rules. Before starting the practice problems, watch this video also to make sure you are ready.

Mario's Math Tutoring - Exponent Rules with Examples [6mins-40secs]

Negative Exponents

Negative exponents can be one of the most difficult concepts when simplifying exponents. Here is a good video clip explaining negative exponents.

The Organic Chemistry Tutor - Negative Exponents Explained! [43secs]

Before we continue, let's watch this video containing several good examples on working some simple problems with negative exponents.

MIP4U - Simplify Exponential Expressions With Negative Exponents - Basic [4mins-44secs]

video by MIP4U

Okay, let's practice these rules on these problems.

Practice Exponent Rules

Unless otherwise instructed, simplify these expressions using the exponent rules on this page. Give your answers in exact, simplified form.

\( x^{-3} \)

Problem Statement

Simplify \( x^{-3} \) using the exponent rules, giving your answer in exact form.

Final Answer

\( 1/x^3 \)

Problem Statement

Simplify \( x^{-3} \) using the exponent rules, giving your answer in exact form.

Solution

The Organic Chemistry Tutor - 3825 video solution

Final Answer

\( 1/x^3 \)

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\(\displaystyle{ \frac{1}{x^{-4}} }\)

Problem Statement

Simplify \(\displaystyle{ \frac{1}{x^{-4}} }\) using the exponent rules, giving your answer in exact form.

Final Answer

\( x^4 \)

Problem Statement

Simplify \(\displaystyle{ \frac{1}{x^{-4}} }\) using the exponent rules, giving your answer in exact form.

Solution

The Organic Chemistry Tutor - 3826 video solution

Final Answer

\( x^4 \)

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Simplify \( - 3^2 \) and \( (-3)^2 \)

Problem Statement

Simplify \( - 3^2 \) and \( (-3)^2 \) using the exponent rules, giving your answer in exact form.

Final Answer

\( - 3^2 = -9 \) and \( (-3)^2 = 9 \)

Problem Statement

Simplify \( - 3^2 \) and \( (-3)^2 \) using the exponent rules, giving your answer in exact form.

Solution

The Organic Chemistry Tutor - 3827 video solution

Final Answer

\( - 3^2 = -9 \) and \( (-3)^2 = 9 \)

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\( x^4 \cdot x^{-9} \)

Problem Statement

Simplify \( x^4 \cdot x^{-9} \) using the exponent rules, giving your answer in exact form.

Final Answer

\( 1/x^5 \)

Problem Statement

Simplify \( x^4 \cdot x^{-9} \) using the exponent rules, giving your answer in exact form.

Solution

The Organic Chemistry Tutor - 3828 video solution

Final Answer

\( 1/x^5 \)

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\(\displaystyle{ \left( \frac{3}{4} \right)^{-2} }\)

Problem Statement

Simplify \(\displaystyle{ \left( \frac{3}{4} \right)^{-2} }\) using the exponent rules, giving your answer in exact form.

Final Answer

\(16/9\)

Problem Statement

Simplify \(\displaystyle{ \left( \frac{3}{4} \right)^{-2} }\) using the exponent rules, giving your answer in exact form.

Solution

The Organic Chemistry Tutor - 3808 video solution

Final Answer

\(16/9\)

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\( (x^3)^4 \)

Problem Statement

Simplify \( (x^3)^4 \) using the exponent rules, giving your answer in exact form.

Final Answer

\( x^{12} \)

Problem Statement

Simplify \( (x^3)^4 \) using the exponent rules, giving your answer in exact form.

Solution

The Organic Chemistry Tutor - 3824 video solution

Final Answer

\( x^{12} \)

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\( (a^5)^7 \)

Problem Statement

Simplify \( (a^5)^7 \) using the exponent rules, giving your answer in exact form.

Final Answer

\( a^{35} \)

Problem Statement

Simplify \( (a^5)^7 \) using the exponent rules, giving your answer in exact form.

Solution

Brian McLogan - 3846 video solution

video by Brian McLogan

Final Answer

\( a^{35} \)

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\( (x^2)^8 \)

Problem Statement

Simplify \( (x^2)^8 \) using the exponent rules, giving your answer in exact form.

Final Answer

\( x^{16} \)

Problem Statement

Simplify \( (x^2)^8 \) using the exponent rules, giving your answer in exact form.

Solution

Brian McLogan - 3842 video solution

video by Brian McLogan

Final Answer

\( x^{16} \)

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\( (3x^2)^3 \)

Problem Statement

Simplify \( (3x^2)^3 \) using the exponent rules, giving your answer in exact form.

Final Answer

\( 27x^6 \)

Problem Statement

Simplify \( (3x^2)^3 \) using the exponent rules, giving your answer in exact form.

Solution

The Organic Chemistry Tutor - 3832 video solution

Final Answer

\( 27x^6 \)

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\( (3a^5b)^4 \)

Problem Statement

Simplify \( (3a^5b)^4 \) using the exponent rules, giving your answer in exact form.

Final Answer

\( 81a^{20}b^4 \)

Problem Statement

Simplify \( (3a^5b)^4 \) using the exponent rules, giving your answer in exact form.

Solution

Brian McLogan - 3843 video solution

video by Brian McLogan

Final Answer

\( 81a^{20}b^4 \)

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\( (2xy^6)^5 \)

Problem Statement

Simplify \( (2xy^6)^5 \) using the exponent rules, giving your answer in exact form.

Final Answer

\( 32x^5y^{30} \)

Problem Statement

Simplify \( (2xy^6)^5 \) using the exponent rules, giving your answer in exact form.

Solution

Brian McLogan - 3847 video solution

video by Brian McLogan

Final Answer

\( 32x^5y^{30} \)

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\( (x^3)^{-4} \)

Problem Statement

Simplify \( (x^3)^{-4} \) using the exponent rules, giving your answer in exact form.

Final Answer

\( 1/x^{12} \)

Problem Statement

Simplify \( (x^3)^{-4} \) using the exponent rules, giving your answer in exact form.

Solution

The Organic Chemistry Tutor - 3809 video solution

Final Answer

\( 1/x^{12} \)

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\( x^4 \cdot x^5 \)

Problem Statement

Simplify \( x^4 \cdot x^5 \) using the exponent rules, giving your answer in exact form.

Final Answer

\( x^9 \)

Problem Statement

Simplify \( x^4 \cdot x^5 \) using the exponent rules, giving your answer in exact form.

Solution

The Organic Chemistry Tutor - 3822 video solution

Final Answer

\( x^9 \)

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\( (x^3)^{-5} \)

Problem Statement

Simplify \( (x^3)^{-5} \) using the exponent rules, giving your answer in exact form.

Final Answer

\( 1/x^{15} \)

Problem Statement

Simplify \( (x^3)^{-5} \) using the exponent rules, giving your answer in exact form.

Solution

The Organic Chemistry Tutor - 3829 video solution

Final Answer

\( 1/x^{15} \)

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\( x^3 \cdot x^{-8} \)

Problem Statement

Simplify \( x^3 \cdot x^{-8} \) using the exponent rules, giving your answer in exact form.

Final Answer

\( 1/x^5 \)

Problem Statement

Simplify \( x^3 \cdot x^{-8} \) using the exponent rules, giving your answer in exact form.

Solution

The Organic Chemistry Tutor - 3810 video solution

Final Answer

\( 1/x^5 \)

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\( (4x^{-5})^2 \)

Problem Statement

Simplify \( (4x^{-5})^2 \) using the exponent rules, giving your answer in exact form.

Final Answer

\( 16/x^{10} \)

Problem Statement

Simplify \( (4x^{-5})^2 \) using the exponent rules, giving your answer in exact form.

Solution

The Organic Chemistry Tutor - 3811 video solution

Final Answer

\( 16/x^{10} \)

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\( \displaystyle{ \frac{x^7}{x^3} } \)

Problem Statement

Simplify \( \displaystyle{ \frac{x^7}{x^3} } \) using the exponent rules, giving your answer in exact form.

Final Answer

\( x^4 \)

Problem Statement

Simplify \( \displaystyle{ \frac{x^7}{x^3} } \) using the exponent rules, giving your answer in exact form.

Solution

The Organic Chemistry Tutor - 3823 video solution

Final Answer

\( x^4 \)

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\(\displaystyle{ \frac{x^7}{x^{12}} }\)

Problem Statement

Simplify \(\displaystyle{ \frac{x^7}{x^{12}} }\) using the exponent rules, giving your answer in exact form.

Final Answer

\( 1/x^5 \)

Problem Statement

Simplify \(\displaystyle{ \frac{x^7}{x^{12}} }\) using the exponent rules, giving your answer in exact form.

Solution

The Organic Chemistry Tutor - 3830 video solution

Final Answer

\( 1/x^5 \)

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\(\displaystyle{ \frac{y^5}{y^{-3}} }\)

Problem Statement

Simplify \(\displaystyle{ \frac{y^5}{y^{-3}} }\) using the exponent rules, giving your answer in exact form.

Final Answer

\( y^8 \)

Problem Statement

Simplify \(\displaystyle{ \frac{y^5}{y^{-3}} }\) using the exponent rules, giving your answer in exact form.

Solution

The Organic Chemistry Tutor - 3812 video solution

Final Answer

\( y^8 \)

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\(\displaystyle{ \frac{x^{-8}}{x^{-11}} }\)

Problem Statement

Simplify \(\displaystyle{ \frac{x^{-8}}{x^{-11}} }\) using the exponent rules, giving your answer in exact form.

Final Answer

\( x^3 \)

Problem Statement

Simplify \(\displaystyle{ \frac{x^{-8}}{x^{-11}} }\) using the exponent rules, giving your answer in exact form.

Solution

The Organic Chemistry Tutor - 3813 video solution

Final Answer

\( x^3 \)

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\(\displaystyle{ \frac{b^{-4}}{b^5} }\)

Problem Statement

Simplify \(\displaystyle{ \frac{b^{-4}}{b^5} }\) using the exponent rules, giving your answer in exact form.

Final Answer

\( 1/b^9 \)

Problem Statement

Simplify \(\displaystyle{ \frac{b^{-4}}{b^5} }\) using the exponent rules, giving your answer in exact form.

Solution

The Organic Chemistry Tutor - 3819 video solution

Final Answer

\( 1/b^9 \)

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\(\displaystyle{ \frac{a^3}{a^7} }\)

Problem Statement

Simplify \(\displaystyle{ \frac{a^3}{a^7} }\) using the exponent rules, giving your answer in exact form.

Final Answer

\( 1/a^4 \)

Problem Statement

Simplify \(\displaystyle{ \frac{a^3}{a^7} }\) using the exponent rules, giving your answer in exact form.

Solution

The Organic Chemistry Tutor - 3820 video solution

Final Answer

\( 1/a^4 \)

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Simplifying Using Exponent Rules

In this video clip, the instructor shows examples of how to use the exponent rules to simplify expressions.

freeCodeCamp.org - College Algebra - Simplifying [21min-32secs]

video by freeCodeCamp.org

Okay, let's practice simplifying on these problems.

Practice Simplifying

Unless otherwise instructed, simplify these expressions using the exponent rules on this page. Give your answers in exact, simplified form.

\( 5-2(x^{-3}x^4)^0 \)

Problem Statement

Simplify \( 5-2(x^{-3}x^4)^0 \) using the exponent rules, giving your answer in exact form.

Final Answer

\( 3 \)

Problem Statement

Simplify \( 5-2(x^{-3}x^4)^0 \) using the exponent rules, giving your answer in exact form.

Solution

Comment: Although in general, his answer is correct, he is making an assumption that \(x \neq 0\). He doesn't need to state this since it is implied by the term \(x^{-3}\). If \(x = 0\) is part of the domain, this term would be \(0^{-3} = 1/0^3 = 1/0\). Remember in algebra, we never want the denominator to be zero. So, in this case the domain does not include zero. So he doesn't have to worry about the case \(0^0\) for this problem.

The Organic Chemistry Tutor - 3814 video solution

Final Answer

\( 3 \)

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\( (-2x^3y^4)^2 \)

Problem Statement

Simplify \( (-2x^3y^4)^2 \) using the exponent rules, giving your answer in exact form.

Final Answer

\( 4x^6y^8 \)

Problem Statement

Simplify \( (-2x^3y^4)^2 \) using the exponent rules, giving your answer in exact form.

Solution

The Organic Chemistry Tutor - 3833 video solution

Final Answer

\( 4x^6y^8 \)

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\( (5x^3)(4x^7) \)

Problem Statement

Simplify \( (5x^3)(4x^7) \) using the exponent rules, giving your answer in exact form.

Final Answer

\( 20x^{10} \)

Problem Statement

Simplify \( (5x^3)(4x^7) \) using the exponent rules, giving your answer in exact form.

Solution

The Organic Chemistry Tutor - 3834 video solution

Final Answer

\( 20x^{10} \)

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\( (7x^6)(5x^4) \)

Problem Statement

Simplify \( (7x^6)(5x^4) \) using the exponent rules, giving your answer in exact form.

Final Answer

\( 35x^{10} \)

Problem Statement

Simplify \( (7x^6)(5x^4) \) using the exponent rules, giving your answer in exact form.

Solution

The Organic Chemistry Tutor - 3835 video solution

Final Answer

\( 35x^{10} \)

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\( (4x^3y^2)(7x^{-4}y^3) \)

Problem Statement

Simplify \( (4x^3y^2)(7x^{-4}y^3) \) using the exponent rules, giving your answer in exact form.

Final Answer

\(\displaystyle{ \frac{28y^5}{x} }\)

Problem Statement

Simplify \( (4x^3y^2)(7x^{-4}y^3) \) using the exponent rules, giving your answer in exact form.

Solution

The Organic Chemistry Tutor - 3836 video solution

Final Answer

\(\displaystyle{ \frac{28y^5}{x} }\)

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\( (3x^{-2}y^3)^2 (4x^5y^{-6})^3 \)

Problem Statement

Simplify \( (3x^{-2}y^3)^2 (4x^5y^{-6})^3 \) using the exponent rules, giving your answer in exact form.

Final Answer

\(\displaystyle{ \frac{576x^{11}}{y^{12}} }\)

Problem Statement

Simplify \( (3x^{-2}y^3)^2 (4x^5y^{-6})^3 \) using the exponent rules, giving your answer in exact form.

Solution

The Organic Chemistry Tutor - 3816 video solution

Final Answer

\(\displaystyle{ \frac{576x^{11}}{y^{12}} }\)

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\(\displaystyle{ \frac{18x^7}{9x^2} }\)

Problem Statement

Simplify \(\displaystyle{ \frac{18x^7}{9x^2} }\) using the exponent rules, giving your answer in exact form.

Final Answer

\( 2x^5 \)

Problem Statement

Simplify \(\displaystyle{ \frac{18x^7}{9x^2} }\) using the exponent rules, giving your answer in exact form.

Solution

Brian McLogan - 3838 video solution

video by Brian McLogan

Final Answer

\( 2x^5 \)

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\(\displaystyle{ \frac{3a^{-4}}{b^{-6}c^3} }\)

Problem Statement

Simplify \(\displaystyle{ \frac{3a^{-4}}{b^{-6}c^3} }\) using the exponent rules, giving your answer in exact form.

Final Answer

\(\displaystyle{ \frac{3b^6}{a^4c^3} }\)

Problem Statement

Simplify \(\displaystyle{ \frac{3a^{-4}}{b^{-6}c^3} }\) using the exponent rules, giving your answer in exact form.

Solution

The Organic Chemistry Tutor - 3815 video solution

Final Answer

\(\displaystyle{ \frac{3b^6}{a^4c^3} }\)

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\(\displaystyle{ \left( \frac{s^4t^5}{st^3} \right)^3 }\)

Problem Statement

Simplify \(\displaystyle{ \left( \frac{s^4t^5}{st^3} \right)^3 }\) using the exponent rules, giving your answer in exact form.

Final Answer

\( s^9 t^6 \)

Problem Statement

Simplify \(\displaystyle{ \left( \frac{s^4t^5}{st^3} \right)^3 }\) using the exponent rules, giving your answer in exact form.

Solution

MIP4U - 3852 video solution

video by MIP4U

Final Answer

\( s^9 t^6 \)

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\(\displaystyle{ \frac{(2x^4)^4}{2x^5} }\)

Problem Statement

Simplify \(\displaystyle{ \frac{(2x^4)^4}{2x^5} }\) using the exponent rules, giving your answer in exact form.

Final Answer

\( 8x^{11} \)

Problem Statement

Simplify \(\displaystyle{ \frac{(2x^4)^4}{2x^5} }\) using the exponent rules, giving your answer in exact form.

Solution

MIP4U - 3853 video solution

video by MIP4U

Final Answer

\( 8x^{11} \)

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\(\displaystyle{ \frac{5x^3y^4}{15x^9y^2} }\)

Problem Statement

Simplify \(\displaystyle{ \frac{5x^3y^4}{15x^9y^2} }\) using the exponent rules, giving your answer in exact form.

Final Answer

\( \displaystyle{ \frac{y^2}{3x^6} } \)

Problem Statement

Simplify \(\displaystyle{ \frac{5x^3y^4}{15x^9y^2} }\) using the exponent rules, giving your answer in exact form.

Solution

Brian McLogan - 3839 video solution

video by Brian McLogan

Final Answer

\( \displaystyle{ \frac{y^2}{3x^6} } \)

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\(\displaystyle{ \frac{21a^3b}{14b^2a^3} }\)

Problem Statement

Simplify \(\displaystyle{ \frac{21a^3b}{14b^2a^3} }\) using the exponent rules, giving your answer in exact form.

Final Answer

\( \displaystyle{ \frac{3}{2b} } \)

Problem Statement

Simplify \(\displaystyle{ \frac{21a^3b}{14b^2a^3} }\) using the exponent rules, giving your answer in exact form.

Solution

Brian McLogan - 3840 video solution

video by Brian McLogan

Final Answer

\( \displaystyle{ \frac{3}{2b} } \)

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\(\displaystyle{ \frac{24x^7y^3}{8x^4y^{-12}} }\)

Problem Statement

Simplify \(\displaystyle{ \frac{24x^7y^3}{8x^4y^{-12}} }\) using the exponent rules, giving your answer in exact form.

Final Answer

\( 3x^3y^{15} \)

Problem Statement

Simplify \(\displaystyle{ \frac{24x^7y^3}{8x^4y^{-12}} }\) using the exponent rules, giving your answer in exact form.

Solution

The Organic Chemistry Tutor - 3837 video solution

Final Answer

\( 3x^3y^{15} \)

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\(\displaystyle{ \frac{45x^4y^{-6}}{27x^{-7}y^5} }\)

Problem Statement

Simplify \(\displaystyle{ \frac{45x^4y^{-6}}{27x^{-7}y^5} }\) using the exponent rules, giving your answer in exact form.

Final Answer

\(\displaystyle{ \frac{5x^{11}}{3y^{11}} }\)

Problem Statement

Simplify \(\displaystyle{ \frac{45x^4y^{-6}}{27x^{-7}y^5} }\) using the exponent rules, giving your answer in exact form.

Solution

Comments:
1. Notice in his solution, he started with the constants and simplified them first. This is a great way to make the problem seem not so complicated and we highly recommend this technique.
2. Although his answer is correct, you could also write the final answer as \( (5/3) (x/y)^11 \)

The Organic Chemistry Tutor - 3817 video solution

Final Answer

\(\displaystyle{ \frac{5x^{11}}{3y^{11}} }\)

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\(\displaystyle{ \frac{8n^{-3}m^7}{12n^2m^{-2}} }\)

Problem Statement

Simplify \(\displaystyle{ \frac{8n^{-3}m^7}{12n^2m^{-2}} }\) using the exponent rules, giving your answer in exact form.

Final Answer

\( \displaystyle{ \frac{2m^9}{3n^5} } \)

Problem Statement

Simplify \(\displaystyle{ \frac{8n^{-3}m^7}{12n^2m^{-2}} }\) using the exponent rules, giving your answer in exact form.

Solution

Brian McLogan - 3841 video solution

video by Brian McLogan

Final Answer

\( \displaystyle{ \frac{2m^9}{3n^5} } \)

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\(\displaystyle{ \frac{18a^3b^{-4}c^{-6}}{30a^7b^5c^{-9}} }\)

Problem Statement

Simplify \(\displaystyle{ \frac{18a^3b^{-4}c^{-6}}{30a^7b^5c^{-9}} }\) using the exponent rules, giving your answer in exact form.

Final Answer

\(\displaystyle{ \frac{3c^3}{5a^4b^9} }\)

Problem Statement

Simplify \(\displaystyle{ \frac{18a^3b^{-4}c^{-6}}{30a^7b^5c^{-9}} }\) using the exponent rules, giving your answer in exact form.

Solution

The Organic Chemistry Tutor - 3818 video solution

Final Answer

\(\displaystyle{ \frac{3c^3}{5a^4b^9} }\)

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\( \displaystyle{ \left( \frac{35x^3y^5}{63x^{-4}y^7} \right)^2 } \)

Problem Statement

Simplify \(\displaystyle{ \left( \frac{35x^3y^5}{63x^{-4}y^7} \right)^2 }\) using the exponent rules, giving your answer in exact form.

Final Answer

\( \displaystyle{ \frac{25x^{14}}{81y^4} } \)

Problem Statement

Simplify \(\displaystyle{ \left( \frac{35x^3y^5}{63x^{-4}y^7} \right)^2 }\) using the exponent rules, giving your answer in exact form.

Solution

The Organic Chemistry Tutor - 3831 video solution

Final Answer

\( \displaystyle{ \frac{25x^{14}}{81y^4} } \)

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\(\displaystyle{ \left( \frac{-2x^0y^6z}{y^4} \right)^3 }\)

Problem Statement

Simplify \(\displaystyle{ \left( \frac{-2x^0y^6z}{y^4} \right)^3 }\) using the exponent rules, giving your answer in exact form.

Final Answer

\( \displaystyle{ \frac{-8y^{18}z^3}{x^{12}} } \)

Problem Statement

Simplify \(\displaystyle{ \left( \frac{-2x^0y^6z}{y^4} \right)^3 }\) using the exponent rules, giving your answer in exact form.

Solution

Brian McLogan - 3848 video solution

video by Brian McLogan

Final Answer

\( \displaystyle{ \frac{-8y^{18}z^3}{x^{12}} } \)

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\( \displaystyle{ \left( \frac{x^3}{2y^5z^8} \right)^4 } \)

Problem Statement

Simplify \(\displaystyle{ \left( \frac{x^3}{2y^5z^8} \right)^4 }\) using the exponent rules, giving your answer in exact form.

Final Answer

\( \displaystyle{ \frac{x^{12}}{16y^{20}z^{32}} } \)

Problem Statement

Simplify \(\displaystyle{ \left( \frac{x^3}{2y^5z^8} \right)^4 }\) using the exponent rules, giving your answer in exact form.

Solution

Brian McLogan - 3844 video solution

video by Brian McLogan

Final Answer

\( \displaystyle{ \frac{x^{12}}{16y^{20}z^{32}} } \)

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\(\displaystyle{ \left( \frac{y}{3xy^{-4}} \right)^{-1} }\)

Problem Statement

Simplify \(\displaystyle{ \left( \frac{y}{3xy^{-4}} \right)^{-1} }\) using the exponent rules, giving your answer in exact form.

Final Answer

\( \displaystyle{ \frac{3x}{y^5} } \)

Problem Statement

Simplify \(\displaystyle{ \left( \frac{y}{3xy^{-4}} \right)^{-1} }\) using the exponent rules, giving your answer in exact form.

Solution

Brian McLogan - 3850 video solution

video by Brian McLogan

Final Answer

\( \displaystyle{ \frac{3x}{y^5} } \)

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\(\displaystyle{ \left( \frac{2xy^2}{x^{-3}y^{-4}} \right)^{-3} }\)

Problem Statement

Simplify \(\displaystyle{ \left( \frac{2xy^2}{x^{-3}y^{-4}} \right)^{-3} }\) using the exponent rules, giving your answer in exact form.

Final Answer

\( \displaystyle{ \frac{1}{8x^{12}y^{18}} } \)

Problem Statement

Simplify \(\displaystyle{ \left( \frac{2xy^2}{x^{-3}y^{-4}} \right)^{-3} }\) using the exponent rules, giving your answer in exact form.

Solution

Brian McLogan - 3845 video solution

video by Brian McLogan

Final Answer

\( \displaystyle{ \frac{1}{8x^{12}y^{18}} } \)

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\(\displaystyle{ \left( \frac{3x^{-4}y}{x^{-3}y^2} \right)^{-2} }\)

Problem Statement

Simplify \(\displaystyle{ \left( \frac{3x^{-4}y}{x^{-3}y^2} \right)^{-2} }\) using the exponent rules, giving your answer in exact form.

Final Answer

\( \displaystyle{ \frac{x^2y^2}{9} } \)

Problem Statement

Simplify \(\displaystyle{ \left( \frac{3x^{-4}y}{x^{-3}y^2} \right)^{-2} }\) using the exponent rules, giving your answer in exact form.

Solution

Brian McLogan - 3849 video solution

video by Brian McLogan

Final Answer

\( \displaystyle{ \frac{x^2y^2}{9} } \)

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\(\displaystyle{ \left( \frac{ 63x^{-3}y^4z^{-5} }{ 35x^8y^{-7}z^{-4} } \right)^2 }\)

Problem Statement

Simplify \(\displaystyle{ \left( \frac{ 63x^{-3}y^4z^{-5} }{ 35x^8y^{-7}z^{-4} } \right)^2 }\) using the exponent rules, giving your answer in exact form.

Final Answer

\(\displaystyle{ \frac{81y^{22}}{25x^{22}z^2} }\)

Problem Statement

Simplify \(\displaystyle{ \left( \frac{ 63x^{-3}y^4z^{-5} }{ 35x^8y^{-7}z^{-4} } \right)^2 }\) using the exponent rules, giving your answer in exact form.

Solution

The Organic Chemistry Tutor - 3821 video solution

Final Answer

\(\displaystyle{ \frac{81y^{22}}{25x^{22}z^2} }\)

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\(\displaystyle{ \left( \frac{2x^3y^2}{-x^2y^5} \right)^{-2} }\)

Problem Statement

Simplify \(\displaystyle{ \left( \frac{2x^3y^2}{-x^2y^5} \right)^{-2} }\) using the exponent rules, giving your answer in exact form.

Final Answer

\( \displaystyle{ \frac{y^6}{4x^2} } \)

Problem Statement

Simplify \(\displaystyle{ \left( \frac{2x^3y^2}{-x^2y^5} \right)^{-2} }\) using the exponent rules, giving your answer in exact form.

Solution

Brian McLogan - 3851 video solution

video by Brian McLogan

Final Answer

\( \displaystyle{ \frac{y^6}{4x^2} } \)

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