step 1 For exercise 22, we have x to the power of 8, y to the power of 4, x to the power of 9, y to y c

Question

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

Name: Problem 37, Chapter 5: Elementary Algebra
Uploaded: 2022-02-14T02:26:18-08:00
Duration: 1 min 18 s
Channel: Victor Salazar
Description: ((x^2)/(y^5))^2

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

Elementary Algebra

Laura Bracken, Ed… 1st Edition

Chapter 5, Problem 37

Instant Answer

Solved by Expert Victor Salazar

02/14/2022

Step 1

In this case, we have: $\left(\frac{x^{2}}{y^{5}}\right)^{2} = \frac{(x^2)^2}{(y^5)^2}$ Now, we can apply the property to each term: $\frac{(x^2)^2}{(y^5)^2} = \frac{x^{2\cdot2}}{y^{5\cdot2}}$ Show more…

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Key Concepts

Power of a Power

This concept states that when an expression that is already raised to an exponent is raised to another exponent, the exponents are multiplied. This rule simplifies expressions by reducing nested exponentiation into a single exponent.

Exponent Rules

Exponent rules encompass the various laws that govern operations with powers, such as multiplying exponents, dividing like bases, and raising a fraction to a power. These principles are fundamental to simplifying and manipulating algebraic expressions involving exponents.

Power of a Quotient

This rule explains that when a fraction is raised to an exponent, both the numerator and the denominator are raised to that exponent separately. It is essential in simplifying expressions where the entire fraction is raised to a power, ensuring each component is treated equally.

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