Question

Explain what you would do first to simplify the expression below.

Justify why, and then state the result of performing this step.

${\left(\frac{{\left(2r^{2}t\right)}^3}{4t^2}\right)}^2$

Answer 1

First step to simplify the expression:

Given expression is ${\left(\frac{{\left(2r^{2}t\right)}^3}{4t^2}\right)}^2$

The first step to simplify the expression to distribute the powers to the numerator and the denominator and further simplify.

For this apply the power rules of exponents that is;${\left({\left(\frac{a}{b}\right)}^m\right)}^n={\left(\frac{a}{b}\right)}^{m\times n}$

Simplify:

$$\begin{gathered} {\left(\frac{{\left(2r^{2}t\right)}^3}{4t^2}\right)}^2=\frac{{\left(2r^{2}t\right)}^{3\times 2}}{{\left(4t^2\right)}^2} \\ =\frac{{\left(2r^{2}t\right)}^6}{\left(16t^4\right)} \end{gathered}$$

Hence, the first step to simplify the expression to distribute the powers to the numerator and the denominator after the first step is${\left(\frac{{\left(2r^{2}t\right)}^3}{4t^2}\right)}^2=\frac{{\left(2r^{2}t\right)}^6}{\left(16t^4\right)}$.