Q.43 - Intermediate Algebra

Question

In the following exercises, simplify using absolute values as necessary. 

$ⓐ \sqrt[4]{16x^8} ⓑ\sqrt[6]{64y^{12}}$

Step-by-Step Solution

Answer

Part(a)$\sqrt[4]{16x^8}=2x^2$

Part(b)$\sqrt[6]{64y^{12}}=2y^2$

Part(a) Step 1. Given information

$ⓐ \sqrt[4]{16x^8}$

Simplify using absolute values as necessary.

Step 2. Explanation

$\begin{array}{l}\text{Since }\\ \Rightarrow {\text{16x}}^8\text{=}{\left(2x^2\right)}^4\\ \Rightarrow \sqrt[4]{16x^8}\\ \Rightarrow \sqrt[4]{{\left(2x^2\right)}^4}\\ \Rightarrow 2x^2\\ \Rightarrow \sqrt[4]{16x^8}=2x^2\end{array}$

Part(b) Step 1. Given information

$ⓑ\sqrt[6]{64y^{12}}$

Simplify using absolute values as necessary.

Step 2. Explanation

$\begin{array}{l}\text{Since }\\ \Rightarrow 64y^{12}={\left(2y^2\right)}^6\\ \Rightarrow \sqrt[6]{{\left(2y^2\right)}^6}\\ \Rightarrow \sqrt[6]{{\left(2y^2\right)}^6}=2y^2\\ \Rightarrow \sqrt[6]{64y^{12}}=2y^2\\ \end{array}$