Question

In the following exercises, simplify.

$\left(a\right)\sqrt[3]{216}\left(b\right)\sqrt[4]{256}$

Short answer

Hence,

$\begin{array}{l}\left(a\right)\sqrt[3]{216}=6\\ \left(b\right)\sqrt[4]{256}=4\end{array}$

Step-by-step solution

Step 1. Given information

$\begin{array}{l}\text{Thegivenexpressionsare}\\ \left(a\right)\sqrt[3]{216}\\ \left(b\right)\sqrt[4]{256}\\ \text{Wehavetosimplifythegivenexpressions.}\end{array}$

Step 2. Simplify the expression in part (a)

$\begin{array}{l}\Rightarrow \sqrt[3]{216}=\sqrt[3]{{\left(6\right)}^3}\left[\because 6^3=216\right]\\ =6\end{array}$

Step 3. Simplify the expression in part (b)

$\begin{array}{l}\Rightarrow \sqrt[4]{256}=\sqrt[4]{{\left(4\right)}^4}\left[\because 4^4=256\right]\\ =4\end{array}$