Question

In the following exercises, simplify.

$\left(a\right)\sqrt[3]{512}\left(b\right)\sqrt[4]{81}\left(c\right)\sqrt[5]{1}$

Short answer

Hence,

$\begin{array}{l}\left(a\right)\sqrt[3]{512}=8\\ \left(b\right)\sqrt[4]{81}=3\\ \left(c\right)\sqrt[5]{1}=1\end{array}$

Step-by-step solution

Step 1. Given information

$\begin{array}{l}\text{Thegivenexpressionsare}\\ \left(a\right)\sqrt[3]{512}\left(b\right)\sqrt[4]{81}\left(c\right)\sqrt[5]{1}\\ \text{Wehavetosimplifythegivenexpressions.}\end{array}$

Step 2. Simplify the expression in part (a)

$\begin{array}{l}\Rightarrow \sqrt[3]{512}=\sqrt[3]{{\left(8\right)}^3}\left[\because 8^3=512\right]\\ =8\end{array}$

Step 3. Simplify the expression in part (b)

$\begin{array}{l}\Rightarrow \sqrt[4]{81}=\sqrt[4]{{\left(3\right)}^4}\left[\because 3^4=81\right]\\ =3\end{array}$

Step 4. Simplify the expression in part (c)

$\begin{array}{l}\Rightarrow \sqrt[5]{1}=\sqrt[5]{{\left(1\right)}^5}\left[\because 1^5=1\right]\\ =1\end{array}$