How do you simplify ##16^(-3/4)##?
February 20th, 2023
##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##
