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 $\frac{r^{\frac{5}{2}} \cdot r^{- \frac{1}{2}}}{r^{- \frac{3}{2}}}$

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

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

Part (a) Step 2.Simplify the expression

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

Part (b) Step 1.Given information

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

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

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

Part (b) Step 2.Simplify the expression

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

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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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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

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
$(a) \frac{r^{\frac{5}{2}} . r^{- \frac{1}{2}}}{r^{- \frac{3}{2}}} (b) (\frac{36 s^{\frac{1}{5}} t^{- \frac{3}{2}}}{s^{- \frac{9}{5}} . t^{\frac{1}{2}}})$