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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. 162 (page 788)

In the following exercises,simplify
$(a) \frac{m^{\frac{7}{4}} . m^{- \frac{5}{4}}}{m^{- \frac{2}{4}}} (b) {(\frac{16 m^{\frac{1}{5}} . n^{\frac{3}{2}}}{81 m^{\frac{9}{5}} . n^{- \frac{1}{2}}})}^{\frac{1}{4}}$

Short Answer

Expert verified

$(a) m (b) \frac{2}{3} m^{- \frac{2}{5}} . n^{\frac{1}{2}}$

Step by step solution

01

Part (a) Step 1.Given information

Consider the given expression, $\frac{m^{\frac{7}{4}} . m^{- \frac{5}{4}}}{m^{- \frac{2}{4}}}$

To simplify the expression,by used product and quotient property that is,

localid="1644852021496" $a^{m} . a^{n} = a^{m + n} a n d (\frac{a^{m}}{a^{n}}) = a^{m - n}$

02

Part (a) Step 2.Simplify the expression

$\frac{m^{\frac{7}{4}} . m^{- \frac{5}{4}}}{m^{- \frac{2}{4}}} = \frac{m^{\frac{7}{4} + (- \frac{5}{4})}}{m^{- \frac{2}{4}}} [S i n c e; a^{m} . a^{n} = a^{m + n}] = \frac{m^{\frac{1}{2}}}{m^{- \frac{2}{4}}} [A d d t h e e x p o n e n t s] = m^{\frac{1}{2} - (- \frac{2}{4})} [S i n c e; \frac{a^{m}}{a^{n}} = a^{m - n}] = m^{1} [S i m p l i f y t h e e x p o n e n t s] = m [s i m p l i f y] T h e r e f o r e, t h e a n s w e r i s m .$

03

Part (b) Step 1 Given information

Consider the given expression, ${(\frac{16 m^{\frac{1}{5}} . n^{\frac{3}{2}}}{81 m^{\frac{9}{5}} . n^{- \frac{1}{2}}})}^{\frac{1}{4}}$

To simplify the expression,by used product and quotient property that is

$a^{m} . a^{n} = a^{m + n} a n d (\frac{a^{m}}{a^{n}}) = a^{m - n}$

04

Part (b) Step 2.Simplify the expression

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Most popular questions from this chapter

Use the Quotient Property to simplify square roots.

$\sqrt{\frac{98 r^{5}}{100}}$

Write with a rational exponent:

(a) $\sqrt{10 m}$

(b) $\sqrt[5]{3 n}$

(c) $3 \sqrt[4]{6 y}$

In the following exercises, solve.

$\sqrt{2 n - 1} - 3 = 0$

In the following exercises, use the Product Property to simplify radical expression $\sqrt{80} .$

Simplify-

(a) $\sqrt{432}$

(b) $\sqrt[3]{625}$

(c) $\sqrt[4]{729}$

See all solutions

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