Chapter 9, Problem 11CCSR

To determine

To determine the correct option from the given options.

Answer to Problem 11CCSR

Correct answer is option C.

Explanation of Solution

Given information:

Given expression is,

  ${\left(\frac{x^4{y}^{-2}}{z^3}\right)}^{-3}$

Here we shall simplify the expression.

Here we shall use the identity ${\left(x^a\right)}^b=x^{ab}$

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

Hence correct answer is option C.