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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 8: Q 154E (page 788)

In the following exercises, simplify:
Part (a): $q^{\frac{2}{3}} . q^{\frac{5}{6}}$
Part (b): ${(h^{6})}^{\frac{4}{3}}$
Part (c): $\frac{n^{\frac{3}{5}}}{n^{\frac{8}{5}}}$

Short Answer

Expert verified

Part (a): On simplifying, we get $q^{\frac{3}{2}}$ .

Part (b): On simplifying, we get $h^{8}$ .

Part (c): On simplifying, we get $\frac{1}{n}$ .

Step by step solution

01

Part (a) Step 1. Given information.

Consider the given question,

$q^{\frac{2}{3}} . q^{\frac{5}{6}}$

Using the product property,

$= q^{\frac{2}{3} + \frac{5}{6}} = q^{\frac{4 + 5}{6}} = q^{\frac{9}{6}} = q^{\frac{3}{2}}$

02

Part (b) Step 1. Given information.

Consider the given question,

${(h^{6})}^{\frac{4}{3}}$

Using the power property,

$= h^{6 脳 \frac{4}{3}} = h^{2 脳 4} = h^{8}$

03

Part (c) Step 1. Given information.

Consider the given question,

$\frac{n^{\frac{3}{5}}}{n^{\frac{8}{5}}}$

Using the quotient property,

$= n^{\frac{3}{5} - \frac{8}{5}} = n^{- \frac{5}{5}} = n^{- 1} = \frac{1}{n}$

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