Question

Simplify:$\left(a\right)\sqrt[3]{27x^{27}}\left(b\right)\sqrt[4]{81q^{28}}$

Short answer

The solution of (a) and (b) are$3x^{9}and3q^7$ respectively.

Step-by-step solution

Part (a) Step 1. Given information

The root:$\sqrt[3]{27x^{27}}$

Part (a) Step 2. Calculation

We have,

$$\begin{gathered} \sqrt[3]{27x^{27}} \\ =\sqrt[3]{{\left(3x^9\right)}^3}rewrite27x^{27}as{\left(3x^9\right)}^3 \\ =3x^9 \end{gathered}$$

Therefore, the solution is$3x^9$

Part (b) Step 1. Given information

The root:$\sqrt[4]{81q^{28}}$

Part (b) Step 2. Calculation

We have,
$$\begin{gathered} \sqrt[4]{81q^{28}} \\ =\sqrt[4]{{\left(3q^7\right)}^4}rewrite81q^{28}as{\left(3q^7\right)}^4 \\ =3q^7 \end{gathered}$$

Therefore, the solution is$3q^7$