Question

Simplify:

$\left(a\right)\sqrt[3]{-625}\left(b\right)\sqrt[4]{-324}.$

Short answer

Part a. After simplifying we get, $-5\sqrt[3]{5}.$

Part b. After simplifying we get,$3\sqrt[4]{-4}.$

Step-by-step solution

Part a Step 1. Rewrite the radicand as a product using perfect cube factors

So,$$\begin{gathered} \sqrt[3]{-625} \\ =\sqrt[3]{{(-5)}^{3}5} \end{gathered}$$

Part a Step 2. Take the cube root

By taking the cube root we get,

$=-5\sqrt[3]{5}$

Part b Step 1. Rewrite the radicand as a product using the largest perfect cube factor

So,

$$\begin{gathered} \sqrt[4]{-324} \\ =\sqrt[4]{{-\left(3\right)}^4{2}^2} \end{gathered}$$

Part b Step 2. Take the quad root

By taking the quad root we get,

$$\begin{gathered} =\sqrt[4]{-{\left(3\right)}^4{2}^2} \\ =3\sqrt[4]{-4} \end{gathered}$$