Q. 8.18 - Intermediate Algebra

Question

Simplify: $\left(a\right) \sqrt[5]{c^{20}} \left(b\right)\sqrt[6]{d^{24}}$

Step-by-Step Solution

Answer

The solution of (a) and (b) are $c^4 and d^4$ respectively.

Part (a) Step 1. Given information

The root: $\sqrt[5]{c^{20}}$

Part (a) Step 2. Calculation

We have,

$$\begin{gathered} \sqrt[5]{c^{20}} \\ =\sqrt[5]{{\left(c^4\right)}^5} \sin ce {\left(c^4\right)}^5=c^{20} \\ =c^4 \sin ce n is odd, \sqrt[n]{a^n}=a \end{gathered}$$

Therefore, the solution is $c^4$

Part (b) Step 1. Given information

The root: $\sqrt[6]{d^{24}}$

Part (b) Step 2. Calculation

We have,

$$\begin{gathered} \sqrt[6]{d^{24}} \\ =\sqrt[6]{{\left(d^4\right)}^6} \sin ce {\left(d^4\right)}^6=d^{24} \\ =d^4 \sin ce d^4 is positive, we do not need an absolute value sign \end{gathered}$$

Therefore, the solution is $d^4$