Simplify: (x^-3 y^5)^-2

Name: Problem 76, Chapter 3: Algebra and Trigonometry
Uploaded: 2021-06-22T20:25:36-08:00
Duration: 1 min 15 s
Channel: Mitchell Dennis
Description: Simplify: (x^-3 y^5)^-2

step 1 Our job today is fairly simple. We've been given a task to simplify an expression. So the expres

Question

Simplify: $\left(x^{-3} y^{5}\right)^{-2}$

   Simplify: $\left(x^{-3} y^{5}\right)^{-2}$

Algebra and Trigonometry

Michael Sullivan 11th Edition

Chapter 3, Problem 76

Instant Answer

Solved by Expert Mitchell Dennis

06/22/2021

Step 1

The power rule states that $(a^m)^n = a^{mn}$. So, we apply this rule to both $x^{-3}$ and $y^{5}$, which gives us $x^{-3*-2}$ and $y^{5*-2}$. Show more…

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Simplify: $\left(x^{-3} y^{5}\right)^{-2}$

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Key Concepts

Power of a Product Rule

This rule states that when a product of expressions is raised to an exponent, each factor is raised to that exponent individually. It is expressed as (ab)^n = a^n * b^n, which helps in simplifying expressions that involve products inside parentheses raised to a power.

Negative Exponent Rule

A negative exponent indicates taking the reciprocal of the base raised to the corresponding positive exponent. The rule is articulated as a^(-n) = 1/(a^n), and it is used to simplify expressions that contain negative powers.

Power to a Power Rule

This rule specifies that when an exponential expression is raised to another power, you multiply the exponents together. It is expressed as (a^m)^n = a^(m*n), which is essential for simplifying nested exponentials.

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