Answered: For Exercise, simplify the expression.

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter2: Solving Equations

Section: Chapter Questions

Problem 19MCQ

See similar textbooks

Related questions

Question

Expert Solution

Step 1

Given expression is,

$\frac{5}{\sqrt[3]{2 x^{2}}}$

Step 2

To simplify the given expression.

Since here cube root is in the denominator of the given expression.

So multiply by the cube root of an expression that will give a perfect cube under the radical of denominator.

In this case the denominator is $\sqrt[3]{2 x^{2}}$ .

So multiply numerator and denominator by $\sqrt[3]{4 x}$ of the given expression.

The expression becomes,

$\frac{5}{\sqrt[3]{2 x^{2}}} = \frac{5}{\sqrt[3]{2 x^{2}}} \frac{\sqrt[3]{4 x}}{\sqrt[3]{4 x}} A f t e r s o l v i n g g e t, \frac{5}{\sqrt[3]{2 x^{2}}} = \frac{5 \times \sqrt[3]{4 x}}{\sqrt[3]{8 x^{3}}} N o w t h e d e n o m i n a t o r o n t h e r i g h t s i d e h a s a p e r f e c t c u b e u n d e r c u b e r o o t . C u b e r o o t o f 8 x^{3} i s 2 x . T h u s a b o v e e x p r e s s i o n b e c o m e s, \frac{5}{\sqrt[3]{2 x^{2}}} = \frac{5 \times \sqrt[3]{4 x}}{2 x}$