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

##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##