Chapter 8: Q. 158 (page 788)

In the following exercises,simplify
$(a) {(625 n^{\frac{8}{3}})}^{\frac{3}{4}} (b) {(9 x^{\frac{2}{5}} y^{\frac{3}{5}})}^{\frac{5}{2}}$

Short Answer

Expert verified

$(a) 125 u^{2} (b) 243 x y^{\frac{3}{2}}$

Step by step solution

Part (a) Step 1.Given information

Consider the given expression ${(625 n^{\frac{8}{3}})}^{\frac{3}{4}}$

To simplify the expression,by used power property that is ${(a^{m})}^{n} = a^{m . n}$ .

Part (a) Step 2. Simplify the expression

${(625 n^{\frac{8}{3}})}^{\frac{3}{4}} = {(625)}^{\frac{3}{4}} . {(n^{\frac{8}{3}})}^{\frac{3}{4} [\sin c e; {(a b)}^{m} = {(a)}^{m} . {(b)}^{m}]} = {(5^{4})}^{\frac{3}{4}} . {(n^{\frac{8}{3}})}^{\frac{3}{4} [\sin c e; 5^{4} = 625]} = {(5)}^{4 . \frac{3}{4}} {(n)}^{\frac{3}{4} \frac{8}{3} [\sin c e; {(a^{m})}^{n} = a^{m n}]} = {(5)}^{\frac{12}{4}} . {(u)}^{\frac{24}{12}} [M u l t i p l a y t h e e x p o n e n t] = {(5)}^{3} . {(u)}^{2} [D i v i d e t h e e x p o n e n t] = 125 u^{2} [S i m p l i f y] T h e r e f o r e, t h e a n s w e r i s 125 u^{2}$

Part (b) Step 1.Given information

Consider the given expression ${(9 x^{\frac{2}{5}} y^{\frac{3}{5}})}^{\frac{5}{2}}$

To simplify the expression,by used power property that is ${(a^{m})}^{n} = (a^{m n})$ .

Part (b) Step 2.Simplify the expression

${(9 x^{\frac{2}{5}} y^{\frac{3}{5}})}^{\frac{5}{2}} = (9^{\frac{5}{2}}) . {(x^{\frac{2}{5}})}^{\frac{5}{2}} . {(y^{\frac{3}{5}})}^{\frac{5}{2}} [S i n c e; {(a b)}^{m} = {(a)}^{m} . {(b)}^{m]} = {(3^{2})}^{\frac{5}{2}} . {(x^{\frac{2}{5}})}^{\frac{5}{2}} . {(y^{\frac{3}{5}})}^{\frac{5}{2} [S i n c e; 2^{2} = 4]} = {(3)}^{2 . \frac{5}{2}} {(x)}^{\frac{5}{2} . \frac{2}{5}} . {(y)}^{\frac{5}{2} . \frac{3}{5} [S i n c e {(a^{m})}^{n} = a^{m . n}]} = {(3)}^{\frac{10}{2}} . {(x)}^{\frac{10}{10}} . {(y)}^{\frac{15}{10}} [M u l t i p l a y t h e e x p o n e n t] = 3^{5} . x . y^{\frac{3}{2}} [D i v i d e t h e e x p o n e n t] = 243 x y^{\frac{3}{2}} [s i m p l i f y] T h e r e f o r e, t h e a n s w e r i s 243 x y^{\frac{3}{2}} .$

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In the following exercises,simplify
$(a) {(625 n^{\frac{8}{3}})}^{\frac{3}{4}} (b) {(9 x^{\frac{2}{5}} y^{\frac{3}{5}})}^{\frac{5}{2}}$

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)(625n83)34(b)(9x25y35)52

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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Calculus

Mechanics Maths

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In the following exercises,simplify
$(a) {(625 n^{\frac{8}{3}})}^{\frac{3}{4}} (b) {(9 x^{\frac{2}{5}} y^{\frac{3}{5}})}^{\frac{5}{2}}$