Q. 592 - Intermediate Algebra

Question

In the following exercises, simplify. Assume all variables are positive.

$\frac{\sqrt[3]{128}}{\sqrt[3]{54}}$

Step-by-Step Solution

Answer

The simplification of the rational radicand $\frac{\sqrt[3]{128}}{\sqrt[3]{54}}$is $\frac{4}{3}.$ 

Step 1. Given Information

We have $\frac{\sqrt[3]{128}}{\sqrt[3]{54}}$

Step 2. Factor the radicand

$\frac{\sqrt[3]{128}}{\sqrt[3]{54}}=\frac{\sqrt[3]{2\times 2\times 2\times 2\times 2\times 2\times 2}}{\sqrt[3]{2\times 3\times 3\times 3}}$

Step 3. Simplify the factor

$$\begin{gathered} =\frac{2\times 2\times \sqrt[3]{2}}{3\times \sqrt[3]{2}} \\ =\frac{4}{3} \end{gathered}$$