Chapter 11.3, Problem 5MCQ

To determine

To find: the expression in radical form.

Answer to Problem 5MCQ

  $5b\sqrt[3]{a^2}$ .

Explanation of Solution

Given:

  ${\left(125a^2{b}^3\right)}^{\frac{1}{3}}.$

Concept used:

Power rules base raised to the power to a power it needs to multiply the exponents.

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

Calculation:

According to the given:

  ${\left(125a^2{b}^3\right)}^{\frac{1}{3}}.$

Try to the make each term as cubic power and used power rule here:

  $\begin{array}{l}\Rightarrow {\left(5^3{a}^2{b}^3\right)}^{\frac{1}{3}}.\\ \Rightarrow 5^{3\times \frac{1}{3}}{a}^{\frac{2}{3}}{b}^{3\times \frac{1}{3}}.\\ \Rightarrow 5b\sqrt[3]{a^2}.\end{array}$

Hence, $5b\sqrt[3]{a^2}$ .