Q. 161 In the following exercises,simpl... [FREE SOLUTION]

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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. 161 (page 788)

In the following exercises,simplify
$(a) \frac{c^{\frac{5}{3}} . c^{- \frac{1}{3}}}{c^{- \frac{2}{3}}} (b) {(\frac{8 x^{\frac{5}{3}} . y^{- \frac{1}{2}}}{27 x^{- \frac{4}{3}} . y^{\frac{5}{2}}})}^{\frac{1}{3}}$

Short Answer

Expert verified

$(a) c^{2} (b) \frac{2 x}{3 y}$

Step by step solution

Part (a) Step 1.Given information

Consider the given expression, $\frac{c^{\frac{5}{3}} . c^{- \frac{1}{3}}}{c^{- \frac{2}{3}}}$

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

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

Part (a) Step 2.Simplify the expression

$\frac{c^{\frac{5}{3}} . c^{- \frac{1}{3}}}{c^{- \frac{2}{3}}} = \frac{c^{\frac{5}{3} + (- \frac{1}{3})}}{c^{- \frac{2}{3}}} [S i n c e; a^{m} . a^{n} = a^{m + n}] = \frac{c^{\frac{4}{3}}}{c^{- \frac{2}{3}}} [A d d t h e e x p o n e n t s] = c^{\frac{4}{3} - (- \frac{2}{3}) [S i n c e; \frac{a^{m}}{a^{n}} = a^{m - n}]} = c^{\frac{4}{3} + \frac{2}{3}} [S i m p l i f y t h e e x p o n e n t s] = c^{2} [S i m p l i f y] T h e r e f o r e, t h e a n s w e r i s c^{2}$

Part (b) Step 1.Given information

Consider the given expression, ${(\frac{8 x^{\frac{5}{3}} . y^{- \frac{1}{2}}}{27 x^{- \frac{4}{3}} . y^{\frac{5}{2}}})}^{\frac{1}{3}}$

To simplify the expression,by used product and quotient property that is, $a^{m} . a^{n} = a^{m + n} a n d (\frac{a^{m}}{a^{n}}) = a^{m - n}$

Part (b) Step 2.Simplify the expression

${(\frac{8 x^{\frac{5}{3}} . y^{- \frac{1}{2}}}{27 x^{- \frac{4}{3}} . y^{\frac{5}{2}}})}^{\frac{1}{3}} = {(\frac{8}{27})}^{\frac{1}{3}} . {(x^{\frac{5}{3} - (- \frac{4}{3})})}^{\frac{1}{3}} . {(y^{- \frac{1}{2} - \frac{5}{2}})}^{\frac{1}{3}} [S i n c e; \frac{a^{m}}{a^{n}} = a^{m - n}] = {[{(\frac{2}{3})}^{3}]}^{\frac{1}{3}} . {(x^{\frac{5}{3} - (- \frac{4}{3})})}^{\frac{1}{3}} . {(y^{- \frac{1}{2} - \frac{5}{2}})}^{\frac{1}{3}} [S i n c e; (\frac{a^{m}}{a^{n}}) = a^{m - n}] = {(\frac{2}{3})}^{3 \frac{1}{3}} . {(x^{3})}^{\frac{1}{3}} . {(y^{- 3})}^{\frac{1}{3}} [S u b s t r a c t t h e e x p o n e n t] = {(\frac{2}{3})}^{\frac{3}{3}} . x^{\frac{3}{3}} . y^{\frac{- 3}{3}} [S i n c e; {(a^{m})}^{n} = a^{m . n}] = \frac{2}{3} . x . y^{- 1 [D i v i d e t h e e x p o n e n t]} = \frac{2 x}{3 y} [S i n c e; a^{- n} = \frac{1}{a^{n}}] T h e r e f o r e, t h e a n s w e r i s \frac{2 x}{3 y}$

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91影视

In the following exercises,simplify
$(a) \frac{c^{\frac{5}{3}} . c^{- \frac{1}{3}}}{c^{- \frac{2}{3}}} (b) {(\frac{8 x^{\frac{5}{3}} . y^{- \frac{1}{2}}}{27 x^{- \frac{4}{3}} . y^{\frac{5}{2}}})}^{\frac{1}{3}}$

Short Answer

Step by step solution

Part (a) Step 1.Given information

Part (a) Step 2.Simplify the expression

Part (b) Step 1.Given information

Part (b) Step 2.Simplify the expression

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91影视

In the following exercises,simplify(a)c53.c-13c-23(b)8x53.y-1227x-43.y5213

Short Answer

Step by step solution

Part (a) Step 1.Given information

Part (a) Step 2.Simplify the expression

Part (b) Step 1.Given information

Part (b) Step 2.Simplify the expression

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

In the following exercises,simplify
$(a) \frac{c^{\frac{5}{3}} . c^{- \frac{1}{3}}}{c^{- \frac{2}{3}}} (b) {(\frac{8 x^{\frac{5}{3}} . y^{- \frac{1}{2}}}{27 x^{- \frac{4}{3}} . y^{\frac{5}{2}}})}^{\frac{1}{3}}$