step 1 All right, guys, for 45, it wants me to simplify the expression of 2x squared over 3Y, all to th

Question

$\left(\frac{3 x^{2}}{4 y^{5}}\right)^{2}$

Name: Problem 39, Chapter 5: Elementary Algebra
Uploaded: 2020-04-20T05:22:49-08:00
Duration: 50 s
Channel: Coach Rye
Description: ((3 x^2)/(4 y^5))^2

   $\left(\frac{3 x^{2}}{4 y^{5}}\right)^{2}$

Elementary Algebra

Laura Bracken, Ed… 1st Edition

Chapter 5, Problem 39

Instant Answer

Solved by Expert Coach Rye

04/20/2020

Step 1

First, we can distribute the exponent to both the numerator and the denominator: $\left(\frac{3 x^{2}}{4 y^{5}}\right)^{2} = \frac{(3x^2)^2}{(4y^5)^2}$ Now, we can apply the power rule for exponents, which states that $(a^m)^n = Show more…

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Key Concepts

Power of a Power Rule

When an expression that already has an exponent is raised to another exponent, the exponents are multiplied together. This rule is key to simplifying parts of an expression that involve nested exponents.

Exponentiation of a Fraction

When raising a fraction to a power, both the numerator and the denominator are raised to that power individually. This principle allows for the systematic simplification of expressions by applying the exponent to each part of the fraction separately.

Power of a Product Rule

The exponent applied to a product distributes to each factor within the product. This rule facilitates the process of raising composite expressions involving constant multiples and variables to a power, breaking the expression into simpler parts.

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