step 1 All right, guys, for 24, we're going to go ahead and solve the expression of A squared, B to the

Question

$$\left(a^{2} b^{-3}\right)^{2}$$

Name: Problem 24, Chapter 5: Algebra for College Students
Uploaded: 2020-04-19T20:14:51-08:00
Duration: 30 s
Channel: Coach Rye
Description: (a^2 b^-3)^2

   $$\left(a^{2} b^{-3}\right)^{2}$$

Algebra for College Students

Mark Dugopolski 5th Edition

Chapter 5, Problem 24

Instant Answer

Solved by Expert Coach Rye

04/19/2020

Step 1

According to the power of a power rule, we multiply the exponents. So, we get $a^{2*2}$ and $b^{-3*2}$. Show more…

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$$\left(a^{2} b^{-3}\right)^{2}$$

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Key Concepts

Power of a Product Rule

This rule states that when a product of terms is raised to a power, each term in the product is raised to that power individually. It allows the expression (xy)^n to be rewritten as x^n * y^n, enabling easier manipulation and simplification of complex expressions.

Product of Powers Rule

When raising an exponential expression to another power, you multiply the exponents. This is summarized by the rule (x^m)^n = x^(m*n), which is essential for simplifying nested exponents in algebraic expressions.

Negative Exponent Rule

A negative exponent indicates the reciprocal of the base raised to the corresponding positive exponent. Specifically, x^-n is equivalent to 1/(x^n), which is useful when rewriting expressions without negative exponents and simplifying algebraic fractions.

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