<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] Simplify it this way:
$
9^\frac{3}{4} \\
= (3^2)^\frac{3}{4}\\
= 3^\frac{2\times 3}{4}\\
= 3^\frac{3}{2}\\
= 3^{\left(1 + \frac{1}{2}\right)}\\
= 3 \times 3^\frac{1}{2}\\
= 3 \sqrt{3}
$
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