Chapter 7, Problem 2MCQ

To determine

To Simplify: The expression ${\left(m^2{p}^5\right)}^3$

Answer to Problem 2MCQ

  ${\left(m^2{p}^5\right)}^3=m^6{p}^{15}$

Explanation of Solution

Given information:

The expression ${\left(m^2{p}^5\right)}^3$

Concept and Formula Used:

Rule of exponent.

  $a^n\times a^n=a^{m+n},{\left(a^n\right)}^m=a^{m\times n}$

BODMAS rule

Calculation:

The given expression is

  $\begin{array}{l}{\left(m^2{p}^5\right)}^3\\ \text{Using }{\left(a^n\right)}^m=a^{m\times n}\\ {\left(m^2{p}^5\right)}^3=\left(m^{2\times 3}{p}^{5\times 3}\right)\\ \text{Simplify}\\ {\left(m^2{p}^5\right)}^3=m^6{p}^{15}\end{array}$

Conclusion:

  ${\left(m^2{p}^5\right)}^3=m^6{p}^{15}$