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Numbers in General Form

Simplify 62...

Question

Simplify
${(\frac{625}{81})}^{- 3 / 4} \times [{(\frac{4}{25})}^{- 3 / 2} \div {(\frac{2}{3})}^{- 3}]$

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Solution

${(\frac{625}{81})}^{- \frac{3}{4}} \times ⎡ ⎣ {(\frac{4}{25})}^{- \frac{3}{2}} \div {(\frac{2}{3})}^{- 3} ⎤ ⎦$

$= {(\frac{5^{4}}{3^{4}})}^{- \frac{3}{4}} \times ⎡ ⎢ ⎣ {(\frac{2^{2}}{5^{2}})}^{- \frac{3}{2}} \div {(\frac{2}{3})}^{- 3} ⎤ ⎥ ⎦$

$= {({(\frac{5}{3})}^{4})}^{- \frac{3}{4}} \times ⎡ ⎢ ⎣ {({(\frac{2}{5})}^{2})}^{- \frac{3}{2}} \times {(\frac{2}{3})}^{3} ⎤ ⎥ ⎦$

$= {(\frac{5}{3})}^{- 3} \times [{(\frac{2}{5})}^{- 3} \times {(\frac{2}{3})}^{3}]$

$= {(\frac{3}{5})}^{3} \times [{(\frac{5}{2})}^{3} \times {(\frac{2}{3})}^{3}]$

$= {(\frac{3 \times 5 \times 2}{5 \times 2 \times 3})}^{3}$

$= {(1)}^{3} = 1$

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