((2 p)/(3 q))^2(4 p)^2

Name: Problem 79, Chapter 5: Elementary Algebra
Uploaded: 2022-02-07T03:13:09-08:00
Duration: 40 s
Channel: Nick Johnson
Description: ((2 p)/(3 q))^2(4 p)^2

step 1 Hello. So what we get here with the negative exponents is the p plus 3q to negative fourth moves

Question

$\left(\frac{2 p}{3 q}\right)^{2}(4 p)^{2}$

   $\left(\frac{2 p}{3 q}\right)^{2}(4 p)^{2}$

Elementary Algebra

Laura Bracken, Ed… 1st Edition

Chapter 5, Problem 79

Instant Answer

Solved by Expert Nick Johnson

02/07/2022

Step 1

First, we can simplify the expression inside the parentheses: $\left(\frac{2 p}{3 q}\right)^{2} = \frac{(2p)^2}{(3q)^2} = \frac{4p^2}{9q^2}$ Now, we can simplify the expression outside the parentheses: $(4p)^2 = 16p^2$ Show more…

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$\left(\frac{2 p}{3 q}\right)^{2}(4 p)^{2}$

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Key Concepts

Power of a Product Rule

The power of a product rule states that when a product is raised to an exponent, each factor in the product is raised to that same exponent individually. This rule is critical for breaking down expressions where multiple factors are multiplied together and then exponentiated.

Power of a Quotient Rule

The power of a quotient rule indicates that when a fraction is raised to an exponent, both the numerator and the denominator are raised to that exponent separately. This is essential for simplifying expressions where a fraction is raised to a power.

Exponent Laws

Exponent laws are fundamental rules in algebra that govern how to manipulate expressions involving powers. They enable the simplification of expressions by providing guidelines for multiplying, dividing, and raising powers to powers.

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