Chapter 7.2, Problem 4AGP

To determine

To Simplify: The Given expression

  $\frac{v^{-3}w{x}^2}{w{y}^{-6}}$

Answer to Problem 4AGP

The simplified expression is $\frac{w^3{x}^2{y}^6}{v^3}$ .

Explanation of Solution

Given information:

  $\frac{v^{-3}w{x}^2}{w{y}^{-6}}$

Concept Used:

Quotient of powers: It states that to divide two powers with same base, subtract the exponent.

For example, let a be any non-zero number and m and n be any integer.

  $\frac{a^m}{a^n}=a^{m-n}$

Negative Exponent Property: $a^{-n}$ is the reciprocal of $a^n$ , where a is a non-zero number and n is an integer.

  $a^{-n}=\frac{1}{a^n}$

Calculation:

  $\frac{v^{-3}w{x}^2}{w{y}^{-6}}$

(Group the powers with the same base)

  $=v^{-3}\left(\frac{w^5}{w^2}\right)x^2\left(\frac{1}{y^{-6}}\right)$

Using Quotient of Powers

  $=v^{-3}{w}^{5-2}{x}^2\left(\frac{1}{y^{-6}}\right)$

Simplify.

  $=v^{-3}{w}^3{x}^2\left(\frac{1}{y^{-6}}\right)$

Using Negative Exponent Property

  $=\frac{w^3{x}^2{y}^6}{v^3}$