Why is $\frac{15\sqrt[4]{125}}{\sqrt[4]{5}}$ $15\sqrt{5}$ and not $15\sqrt[4]{25}$? I have an expression I am to simplify:
$$\frac{15\sqrt[4]{125}}{\sqrt[4]{5}}$$
I arrived at $15\sqrt[4]{25}$. My textbook tells me that the answer is in fact $15\sqrt{5}$. Here is my thought process:
$\frac{15\sqrt[4]{125}}{\sqrt[4]{5}}$ = $\frac{15*\sqrt[4]{5}*\sqrt[4]{25}}{\sqrt[4]{5}}$ = 
(cancel out $\sqrt[4]{5}$ present in both numerator and denominator)
leaving:
$$15\sqrt[4]{25}$$
Where did I go wrong and how can I arrive at $15\sqrt{5}$?

It turns out that $\sqrt[4]{25}=\sqrt{5}$. This is because $25=5^2$, so that $\sqrt[4]{25}=\sqrt[4]{5^2}=(5^2)^{1/4}=5^{1/2}=\sqrt{5}.$ So, you are correct, as is the book.
