Q. 257 - Intermediate Algebra

Question

In the following exercises, simplify. 

$\frac{\sqrt[3]{48a^3{b}^6}}{\sqrt[3]{3a^{-1}{b}^3}}$

Step-by-Step Solution

Answer

The simplified form is $2a{b}^3\sqrt{2a}$.

Step 1. Given information.

The given expression is 

$\frac{\sqrt[3]{48a^3{b}^6}}{\sqrt[3]{3a^{-1}{b}^3}}$.

Step 2. Simplifying.

Now, to simplify the expression first we will rewrite the expression using the quotient property.

$\frac{\sqrt[3]{48a^3{b}^6}}{\sqrt[3]{3a^{-1}{b}^3}}=\sqrt[3]{\frac{48a^3{b}^6}{3a^{-1}{b}^3}}$

Then removing the common factors. 

$\sqrt[3]{\frac{48a^3{b}^6}{3a^{-1}{b}^3}}=\sqrt[3]{16a^4{b}^3}$

On simplifying we get, 

$\sqrt[3]{16a^4{b}^3}=2a{b}^3\sqrt{2a}$

Hence, the simplified form is $2a{b}^3\sqrt{2a}$.