Question

Simplify:

$\left(a\right)\sqrt[3]{-64}\left(b\right)\sqrt[4]{-81}.$

Short answer

Part a. After simplifying we get, $-4.$

Part b. After simplifying we get that there is no real number.

Step-by-step solution

Part a Step 1. Given Information

The given radical is $\sqrt[3]{-64}.$

We have to simplify it.

Part a Step 2. Rewrite the radicand as a product using perfect cube factors

So,$$\begin{gathered} =\sqrt[3]{-64} \\ =\sqrt[3]{{(-4)}^3} \end{gathered}$$

Part a Step 3. Take the cube root

By taking the cube root we get,

$$\begin{gathered} =\sqrt[3]{{(-4)}^3} \\ =-4 \end{gathered}$$

Part b Step 1. Given Information

The given radical is$\sqrt[4]{-81}.$

We have to simplify it.

Part b Step 2. Rewrite the radicand as a product using the largest perfect cube factor

So,

$$\begin{gathered} \sqrt[4]{-81} \\ =\sqrt[4]{{(-3)}^4} \end{gathered}$$

There is no real number nwhere$n^4=-81.$