Indices Question | Find the value of n.

Question

I am having trouble working out this question and I wanted to know if someone could explain how to work it out.

Given that $$81^{-\frac34} = 3^n.$$ Find the value of n.

This is what I have done so far and I don't know where to go from here.

$81^{-\frac34} = (9^2)^{-\frac34} = 9^{2\times -\frac34}$

Thanks.

Answer 1

HINT: since $$3^4=81$$ we have $$(3^4)^{-3/4}=3^{-3}$$

Answer 2

We have $$3^{4\cdot\left(-\frac{3}{4}\right)}=3^n$$ or $$3^{-3}=3^n$$ or $$n=-3$$