<s>[INST] Simplifying $9^{3/4}$, I get $3\sqrt[4]{9}$, but that's not the answer. Why? I am trying to simplify:
$9^\frac{3}{4}$
So this is what I did:
$9^\frac{3}{4} = \sqrt[4]{9^3}$
$\sqrt[4]{3*3*3*3*3*3}$
$3\sqrt[4]{3*3}$
$3\sqrt[4]{9}$
$3\sqrt[4]{3^2}$
I don't see how I can simplify this even more, however the answer I provided is incorrect. How can I simplify this even more?
 [/INST] We know that $9=3^2$ .So, $$\sqrt [4]{9^3} =\sqrt [4]{(3^2)^3} =\sqrt [4]{3^2*3^2*3^2} =\sqrt {3*3*3*3*3*3} $$ After this you have proceeded correctly. You can simplify the last step as: $$ 3\sqrt [4]{3^2} =3\times 3^{2/4} =3\times 3^{1/2} =3\sqrt {3} $$ Hope it helps. 
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