Question

Simplify:$\left(a\right)\sqrt[3]{125q^9}\left(b\right)\sqrt[5]{243q^{25}}$

Short answer

The solution of (a) and (b) are$5q^{3}and3q^5$ respectively.

Step-by-step solution

Part (a) Step 1. Given information

The root:$\sqrt[3]{125q^9}$

Part (a) Step 2. Calculation

We have,

$$\begin{gathered} \sqrt[3]{125q^9} \\ =\sqrt[3]{{\left(5q^3\right)}^3}rewrite125q^{9}as{\left(5q^3\right)}^3 \\ =5q^3 \end{gathered}$$

Therefore, the solution is$5q^3$

Part (b) Step 1. Given information

The root:$\sqrt[5]{243q^{25}}$

Part (b) Step 2. Calculation

We have,

$$\begin{gathered} \sqrt[5]{243q^{25}} \\ =\sqrt[5]{{\left(3q^5\right)}^5}rewrite243q^{25}as{\left(3q^5\right)}^5 \\ =3q^5 \end{gathered}$$

Therefore, the solution is$3q^5$