Chapter 11: Q. 156 (page 1069)

Simplify
(a) ${(\frac{1}{2} y^{2})}^{3} {(\frac{2}{3} y)}^{2}$
(b) ${(\frac{1}{2} j^{2})}^{5} {(\frac{2}{5} j^{3})}^{2}$

Short Answer

Expert verified

Simplified expressions are

(a) $\frac{y^{8}}{18}$

(b) $\frac{j^{16}}{200}$

Step by step solution

part (a) Step 1 Given information

${(\frac{1}{2} y^{2})}^{3} {(\frac{2}{3} y)}^{2}$

part (a) Step 2

${(\frac{1}{2} y^{2})}^{3} {(\frac{2}{3} y)}^{2} = {(\frac{1}{2})}^{3} {(y^{2})}^{3} {(\frac{2}{3})}^{2} {(y)}^{2} = \frac{1}{2^{3}} \times y^{2 \times 3} \times \frac{2^{2}}{3^{2}} \times y^{2} = \frac{1}{8} \times y^{6} \times \frac{4}{9} \times y^{2} = \frac{1}{18} \times y^{6 + 2} = \frac{y^{8}}{18}$

part (b) Step 1 Given information

${(\frac{1}{2} j^{2})}^{5} {(\frac{2}{5} j^{3})}^{2}$

part (b) Step 2

${(\frac{1}{2} j^{2})}^{5} {(\frac{2}{5} j^{3})}^{2} = {(\frac{1}{2})}^{5} {(j^{2})}^{5} {(\frac{2}{5})}^{2} {(j^{3})}^{2} = \frac{1}{2^{5}} \times j^{2 \times 5} \times \frac{2^{2}}{5^{2}} \times j^{3 \times 2} = \frac{1}{32} \times j^{10} \times \frac{4}{25} \times j^{6} = \frac{1}{200} \times j^{10 + 6} = \frac{j^{16}}{200}$

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Simplify
(a) ${(\frac{1}{2} y^{2})}^{3} {(\frac{2}{3} y)}^{2}$
(b) ${(\frac{1}{2} j^{2})}^{5} {(\frac{2}{5} j^{3})}^{2}$

Short Answer

Step by step solution

part (a) Step 1 Given information

part (a) Step 2

part (b) Step 1 Given information

part (b) Step 2

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Simplify(a)12y2323y2(b)12j2525j32

Short Answer

Step by step solution

part (a) Step 1 Given information

part (a) Step 2

part (b) Step 1 Given information

part (b) Step 2

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Simplify
(a) ${(\frac{1}{2} y^{2})}^{3} {(\frac{2}{3} y)}^{2}$
(b) ${(\frac{1}{2} j^{2})}^{5} {(\frac{2}{5} j^{3})}^{2}$