How do you simplify #32^(-2/5)#?

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Answer 1 · 2017-01-26T19:46:13

#1/4#

Recall that:

#a^-b = 1/a^b#

and

#a^(b/c) = root(c)(a^b)#

combined, it is #a^(-b/c) = 1/(root(c)(a^b))#

The above apply where defined.

Therefore, #32^(-2/5) = 1/(root(5)(32^2)#

#=1/((root(5)(32))^2# #=1/2^2 = 1/4#, because #color(red)2^5 = 32#.