Chapter 5: Q. 157 (page 522)

Simplify
(a) ${(2 r^{- 2})}^{3} {(4^{- 1} r)}^{2}$ (b) ${(3 x^{- 3})}^{3} {(3^{- 1} x^{5})}^{4}$

Short Answer

Expert verified

Simplified expressions are

(a) $\frac{1}{2 r^{4}}$

(b) $\frac{x^{11}}{3}$

Step by step solution

part (a) Step 1 Given information

${(2 r^{- 2})}^{3} {(4^{- 1} r)}^{2}$

part (a) Step 2

${(2 r^{- 2})}^{3} {(4^{- 1} r)}^{2} = {(2)}^{3} {(r^{- 2})}^{3} {(4^{- 1})}^{2} {(r)}^{2} = 8 \times r^{- 2 \times 3} \times 4^{- 1 \times 2} \times r^{2} = 8 \times r^{- 6} \times 4^{- 2} \times r^{2} = 8 \times r^{- 6 + 2} \times \frac{1}{16} = \frac{r^{- 4}}{2} = \frac{1}{2 r^{4}}$

part (b) Step 1 Given information

${(3 x^{- 3})}^{3} {(3^{- 1} x^{5})}^{4}$

part (b) Step 2

${(3 x^{- 3})}^{3} {(3^{- 1} x^{5})}^{4} = {(3)}^{3} {(x^{- 3})}^{3} {(3^{- 1})}^{4} {(x^{5})}^{4} = 27 \times x^{- 3 \times 3} \times 3^{- 1 \times 4} \times x^{5 \times 4} = 27 \times x^{- 9} \times \frac{1}{3^{4}} \times x^{20} = 27 \times x^{- 9 + 20} \times \frac{1}{81} = \frac{x^{11}}{3}$

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Simplify
(a) ${(2 r^{- 2})}^{3} {(4^{- 1} r)}^{2}$ (b) ${(3 x^{- 3})}^{3} {(3^{- 1} x^{5})}^{4}$

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) ${(2 r^{- 2})}^{3} {(4^{- 1} r)}^{2}$ (b) ${(3 x^{- 3})}^{3} {(3^{- 1} x^{5})}^{4}$