Q. 231 - Intermediate Algebra

Question

Simplify:

$\left(7\sqrt[3]{4}\right)\left(-3\sqrt[3]{18}\right)$

Step-by-Step Solution

Answer

The value of the given expression 

$-42\sqrt[3]{9}$

Step 1. Given information

The given expression is:

$\left(7\sqrt[3]{4}\right)\left(-3\sqrt[3]{18}\right)$

Step 2. Simplifying the expression

We know that ,

 $\sqrt[n]{a}·\sqrt[n]{b}=\sqrt[n]{ab}$

Then,

$$\begin{gathered} \left(7\sqrt[3]{4}\right)\left(-3\sqrt[3]{18}\right) \\ -7·3\left(\sqrt[3]{4·18}\right) \\ -21\left(\sqrt[3]{72}\right) \\ -21\left(\sqrt[3]{8·9}\right) \\ -21·2\sqrt[3]{9} [\sqrt[3]{8}=2] \\ -42\sqrt[3]{9} \end{gathered}$$