Q. 159 In the following exercises,simpl... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 159 (page 1069)

In the following exercises,simplify
$(a) \frac{r^{\frac{5}{2}} . r^{- \frac{1}{2}}}{r^{- \frac{3}{2}}} (b) (\frac{36 s^{\frac{1}{5}} t^{- \frac{3}{2}}}{s^{- \frac{9}{5}} . t^{\frac{1}{2}}})$

Short Answer

Expert verified

$(a) r^{\frac{7}{2}} (b) 36 s^{2} t^{- 2}$

Step by step solution

Part (a) Step 1.Given information

Consider the expression $\frac{r^{\frac{5}{2}} 路 r^{- \frac{1}{2}}}{r^{- \frac{3}{2}}}$

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

$a^{m} 路 a^{n} = a^{m + n} a n d \frac{a^{m}}{a^{n}} = a^{m - n}$

Part (a) Step 2.Simplify the expression

$\frac{r^{\frac{5}{2}} 路 r^{- \frac{1}{2}}}{r^{- \frac{3}{2}}} = \frac{r^{\frac{5}{2} - \frac{1}{2}}}{r^{- \frac{3}{2}}} [\sin c e; a^{m} 路 a^{n} = a^{m + n]} = \frac{r^{2}}{r^{- \frac{3}{2}}} [A d d t h e e x p o n e n t] = r^{2 - (- \frac{3}{2})} [S i n c e; a^{\frac{m}{n}} = a^{m - n}] = r^{2 + \frac{3}{2}} [S i m p l i f y t h e e x p o n e n t] = r^{\frac{7}{2}} [S i m p l i f y] T h e r e f o r e, t h e a n s w e r i s r^{\frac{7}{2}}$

Part (b) Step 1.Given information

Consider the expression $(\frac{36 s^{\frac{1}{5}} t^{- \frac{3}{2}}}{s^{- \frac{9}{5}} 路 t^{\frac{1}{2}}})$

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

$a^{m} 路 a^{n} = a^{m + n} a n d \frac{a^{m}}{a^{n}} = a^{m - n}$

Part (b) Step 2.Simplify the expression

$(\frac{36 s^{\frac{1}{5}} t^{- \frac{3}{2}}}{s^{- \frac{9}{5}} 路 t^{\frac{1}{2}}}) = (36) 路 (s^{\frac{1}{5} - (- \frac{9}{5})}) 路 (t^{- \frac{3}{2} - \frac{1}{2}}) [S i n c e \frac{a^{m}}{a^{n}} = a^{m - n}] = (6^{2}) 路 (s^{\frac{1}{5} - (- \frac{9}{5})}) 路 (t^{- \frac{3}{2} - \frac{1}{2}}) [\sin c e; 6^{2} = 36] = (6^{2}) 路 (s^{2}) 路 (t^{- 2}) [s u b s t r a c t t h e e x p o n e n t] = {(6)}^{2} 路 {(s)}^{2} 路 {(t)}^{- 2} [\sin c e; {(a^{m})}^{n} = a^{m n}] = 36 s^{2} t^{- 2} [m u l t i p l a y t h e e x p o n e n t] T h e r e f o r e, t h e a n s w e r i s 36 s^{2} t^{- 2}$

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91影视

In the following exercises,simplify
$(a) \frac{r^{\frac{5}{2}} . r^{- \frac{1}{2}}}{r^{- \frac{3}{2}}} (b) (\frac{36 s^{\frac{1}{5}} t^{- \frac{3}{2}}}{s^{- \frac{9}{5}} . t^{\frac{1}{2}}})$

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)r52.r-12r-32(b)36s15t-32s-95.t12

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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Most popular questions from this chapter

Recommended explanations on Math Textbooks

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In the following exercises,simplify
$(a) \frac{r^{\frac{5}{2}} . r^{- \frac{1}{2}}}{r^{- \frac{3}{2}}} (b) (\frac{36 s^{\frac{1}{5}} t^{- \frac{3}{2}}}{s^{- \frac{9}{5}} . t^{\frac{1}{2}}})$