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Question
Compute:
`(27)^(2/3)÷(81/16)^(-1/4)`
Sum
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Solution
`(27)^(2/3) ÷ (81/16)^(-1/4) = (3^3)^(2/3) ÷ (3^4/2^4)^(-1/4)`
`= 3^(3 xx 2/3) ÷ 3^(-1/4 xx 4)/2^(-1/4 xx 4) = 3^2 ÷ 3^-1/2^-1`
`= 3^2 xx 2^-1/3^-1`
`= 3^(2 + 1) xx 2^-1 = 3^3 xx 1/2^ + 1`
`= (3 xx 3 xx 3)/2 = 27/2 = 13 1/2`
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