Chapter 1.3, Problem 9QR

To determine

Tosimplify:The given exponential expression $\frac{{\left(x^{-3}{y}^2\right)}^2}{{\left(x^4{y}^3\right)}^3}$ .

Answer to Problem 9QR

The simplified value of expression $\frac{{\left(x^{-3}{y}^2\right)}^2}{{\left(x^4{y}^3\right)}^3}$ is $\frac{1}{x^{18}{y}^5}$ .

Explanation of Solution

Given information:The expression is $\frac{{\left(x^{-3}{y}^2\right)}^2}{{\left(x^4{y}^3\right)}^3}$ .

Formula used: The rule of exponents:

  ${\left(x^a\right)}^b=x^{ab}$ and $\frac{x^a}{x^b}=x^{a-b}$

Calculation:

Use the exponents rule and simplify the expression.

  $\begin{array}{c}\frac{{\left(x^{-3}{y}^2\right)}^2}{{\left(x^4{y}^3\right)}^3}=\frac{\left(x^{-6}{y}^4\right)}{\left(x^{12}{y}^9\right)}\\ =x^{-6-12}{y}^{4-9}\\ =x^{-18}{y}^{-5}\\ =\frac{1}{x^{18}{y}^5}\end{array}$

Therefore, the simplified value of expression $\frac{{\left(x^{-3}{y}^2\right)}^2}{{\left(x^4{y}^3\right)}^3}$ is $\frac{1}{x^{18}{y}^5}$ .