Question

Simplify by expressing fractional exponents instead of radicals.

Answer 1

\[\sqrt[8]{x^2y^4}\]

Answer 2

remove common factors, namely 2 and get
\[\sqrt[4]{xy^2}\]
no need for exponentials for this problem

Answer 3

by "remove common factors" i should say "factors in common in the index and radicand"

Answer 4

I don't understand. could you please explain.

Answer 5

yes
the index is 8
the radicand (the expression inside the radical) is \(x^2y^4\) and each exponent has a factor of 2
so you can divide each by a factor of 2
8 divided by 2 is 4,
2 divided by 2 is 1,
4 divided by 2 is 2,
you get
\[\sqrt[4]{xy^2}\]

Answer 6

you can also rewrite at
\[(x^2y^4)^{\frac{1}{8}}=x^{\frac{2}{8}}\times y^{\frac{4}{8}}=x^{\frac{1}{4}}\times y^{\frac{2}{4}}\] if you like, but it seems like a large waste of time

Answer 7

or even \(x^{\frac{1}{4}}\times y^{\frac{1}{2}}\)

Answer 8

could you please help me with another. it is:
\[\sqrt[8]{y^2}\]