Chapter 6.2, Problem 17WE

To determine

To calculate: The simplified form of the expression ${\left(\frac{a}{6}\right)}^2$.

Answer to Problem 17WE

The simplified form of the expression ${\left(\frac{a}{6}\right)}^2$ is $\frac{a^2}{36}$.

Explanation of Solution

Given information:

The expression ${\left(\frac{a}{6}\right)}^2$.

Formula used:

Law of exponent for a quotient raised to power m where m is a positive integer is ${\left(\frac{a}{b}\right)}^m=\frac{a^m}{b^m}$.

Calculation:

Consider the expression ${\left(\frac{a}{6}\right)}^2$.

Recall that law of exponent for a quotient raised to power m where m is a positive integer is ${\left(\frac{a}{b}\right)}^m=\frac{a^m}{b^m}$.

Apply it,

  $\begin{array}{c}{\left(\frac{a}{6}\right)}^2=\frac{a^2}{6^2}\\ =\frac{a^2}{36}\end{array}$

Thus, the simplified form of the expression ${\left(\frac{a}{6}\right)}^2$ is $\frac{a^2}{36}$.