Question

Simplify:$\left(a\right)\sqrt[3]{-216}\left(b\right)\sqrt[4]{-81}\left(c\right)\sqrt[5]{1024}$

Short answer

The solutions of (a) is $-6$, (b) is no real number and (c) is$-4$

Step-by-step solution

Part (a). Step 1. Given information

The root:$\sqrt[3]{-216}$

Part (a) Step 2. Calculation

We have,

$$\begin{gathered} \sqrt[3]{-216} \\ =-6 \end{gathered}$$

Since, $-6^3=-216$

Therefore, the solution is$-6$

Part (b). Step 1. Given information

The root:$\sqrt[4]{-81}$

Part (b) Step 2. Calculation

We have,

$$\begin{gathered} \sqrt[4]{-81} \\ Notarealnumber \end{gathered}$$

No real number is raised to the fourth power is negative.

Part (c). Step 1. Given information

The root:$\sqrt[5]{-1024}$

Part (c) Step 2. Calculation

We have,

$$\begin{gathered} \sqrt[5]{-1024} \\ =-4 \end{gathered}$$

Since, ${(-4)}^5=-1024$

Therefore, the solution is$-4$