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Factorisation by Regrouping Terms

Simplify: 8...

Question

Simplify: ${(81)}^{\frac{3}{4}} - {(\frac{1}{32})}^{\frac{- 2}{5}} + 8^{\frac{1}{3}} {(\frac{1}{2})}^{- 1}$

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Solution

given, ${(81)}^{\frac{3}{4}} - {(\frac{1}{32})}^{\frac{- 2}{5}} + 8^{\frac{1}{3}} {(\frac{1}{2})}^{- 1}$

$= {(3^{4})}^{\frac{3}{4}} - {(\frac{1}{2^{5}})}^{\frac{- 2}{5}} + {(2^{3})}^{\frac{1}{3}} {(\frac{1}{2})}^{- 1}$

$= 3^{3} - {(2^{- 5})}^{\frac{- 2}{5}} + 2 + {(2^{- 1})}^{- 1}$

$= 3^{3} - 2^{2} + 2 + 2$

$= 27 - 4 + 4 = 27$

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