Maths question indecies? ?

A) express 8^1/2 as a power of 2


B) express √3 as a power of 9


C) express 1/4√2 as a power of 2





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Maths question indecies? ?
A) express 8^1/2 as a power of 2


8^{1/2} = (2^3)^{1/2} = 2^{3/2}


B) express √3 as a power of 9


sqrt(3) = 9^{1/4}


C) express 1/4√2 as a power of 2


1/4√2 = 2^{- 5/2}
Reply:A = 8^1/2 = sqrt8 = sqrt4*sqrt2 = 2*sqrt2 = (2^1)(2^1/2) = 2^3/2.





B. sqrt9 = 3. Therefore sqrt3 = sqrt(sqrt9) = (9^1/2)^1/2 = 9^1/4.





1/4 = 2^-2.


sqrt 2 = 2^1/2.





1/4sqrt2 = 2^-2*2^1/2 = 2^(-2+1/2) = 2^-3/2.

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