How do you simplify #16^(-3/4)#?

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Answer 1 · 2015-04-09T05:23:14

#1/8#

Firstly, you should change the 16 into the simplest base-power form.

#16=2^4#

#16^(-3/4) = (2^4)^(-3/4)#

As we remember, the formula of multiplying powers, where
#(a^m)^n = a^(mn)#

Therefore,
#(2^4)^(-3/4) = 2^(-12/4)=2^-3#

Here we can apply the Indew law of #a^-n=1/a^n#
Hence, #2^-3=1/2^3=1/8#

#16^(-3/4)=1/8#