854/VB02. problem / Math - Solved Math Problems

MR-854 / 1d. problem

Simplify the following expression:

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

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

$= {({(\frac{4}{3})}^{- 1} - \frac{1}{2^{2}})}^{- 3}$

$= {({(\frac{3}{4})}^{1} - \frac{1}{4})}^{- 3}$

$= {(\frac{3}{4} - \frac{1}{4})}^{- 3}$

$= {(\frac{2}{4})}^{- 3}$

$= {(\frac{4}{2})}^{3}$

$= \frac{4^{3}}{2^{3}}$

$= \frac{64}{8}$

$= 8$

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