Q. 8.21 - Intermediate Algebra

Question

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

Step-by-Step Solution

Answer

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

Part (a) Step 1. Given information

The root: $\sqrt[3]{27x^{27}}$

Part (a) Step 2. Calculation

We have,

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

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

Therefore, the solution is $3q^7$