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How do you write #1/(3sqrt2^-n)# as a fractional exponent?

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1 Answer

Aug 2, 2015

#color(red)(1/(3(sqrt2)^(-n)) = 2^(n/2)/3)#

Explanation:

#1/x^(-n)= x^n#, so

#1/(3(sqrt2)^(-n)) = (sqrt2)^n/3 = (2^(1/2))^n/3#

Also, #(x^a)^b = x^(ab)#, so

#(2^(1/2))^n/3 = 2^(n/2)/3#

∴ #1/(3(sqrt2)^(-n)) = 2^(n/2)/3#

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