Chapter SH, Problem 9.6.1EP

To determine

  ${\left(3^2\right)}^5$ need to simplify.

Answer to Problem 9.6.1EP

  ${\left(3^2\right)}^5=59049$

Explanation of Solution

Given:

  ${\left(3^2\right)}^5$

Concept Used:

According to powers of power property:

  ${\left(a^m\right)}^n=a^{mn}$

Calculation:

The given number is: ${\left(3^2\right)}^5$

Here,

  $\begin{array}{l}m=2\\ n=5\end{array}$

By using the powers of power property:

  ${\left(a^m\right)}^n=a^{mn}$

Put the given values:

  $\begin{array}{l}{\left(3^2\right)}^5=3^{2\times 5}\\ {\left(3^2\right)}^5=3^{10}\\ {\left(3^2\right)}^5=59049\end{array}$

Conclusion:

Hence, ${\left(3^2\right)}^5=3^{10}$ .