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Evaluate (i) (32)^((1)/(5)) +(-7)^(0)...

Evaluate
(i) `(32)^((1)/(5)) +(-7)^(0) + (64)^((1)/(2))`
(ii) `(0.00032)^(-(2)/(3))`
(iii) `((64)/(125))^(-(2)/(3))`.

Text Solution

Verified by Experts

(i) ` ( 32) ^( 1)/(5) + ( - 7 ) ^( 0 ) + ( 64 ) ^(( 1)/(2) )`
` = ( 2^(5)) ^((1)/(5)) + 1 + sqrt ( 64) " " [ because a^( 0 ) = 1 ] `
` = 2^(( 5 xx (1)/(5))) + 1 + 8 = 2 + 1 + 8 = 11 . `
(ii) `(0.00032)^(-(2)/(5)) = (1)/(0.00032)^((2)/(5))" "[because a^(-n) = (1)/(a^(n))]`
`= (1)/([(0.2)^(5)]^((2)/(5))) = (1)/((0.2)^((5xx(2)/(5)))) = (1)/((0.2)^(2))`
` = (1)/(0.04) = (100)/(4) = 25`
(iii) `((64)/(125))^(-(2)/(5)) = ((4^(3))/(5^(3))) = [((4)/(5))^(3)]^((-2)/(3))`
` = ((4)/(5))^([3xx(-(2)/(3))]) = ((4)/(5))^(-2) = ((5)/(4))^(2) = (25)/(16)`
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