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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 9: Q 489. (page 1125)

Simplify :
(a) $\sqrt[3]{\frac{625 u^{10}}{v^{3}}}$
(b) $\sqrt[4]{\frac{729 c^{21}}{d^{8}}}$

Short Answer

Expert verified

Part (a) : $\frac{5 u^{3} \sqrt[3]{5 u}}{v}$

Part (b) :role="math" localid="1650686524580" $\frac{3 c^{5} \sqrt[4]{9 c}}{d^{2}}$

Step by step solution

01

Part (a) Step 1: Given information

The given expression is $\sqrt[3]{\frac{625 u^{10}}{v^{3}}}$

02

Part (a) Step 2: Simplification

$\sqrt[3]{\frac{625 u^{10}}{v^{3}}} = \sqrt[3]{\frac{5^{4} u^{10}}{v^{3}}} = \frac{5 u^{3} \sqrt[3]{5 u}}{v}$

03

Part (b) Step 1: Given information

The given expression is $\sqrt[4]{\frac{729 c^{21}}{d^{8}}}$

04

Part (b) Step 2: Simplification

$\sqrt[4]{\frac{729 c^{21}}{d^{8}}} = \sqrt[4]{\frac{3^{6} c^{21}}{d^{8}}} = \frac{3 c^{5} \sqrt[4]{9 c}}{d^{2}}$

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