Question

Simplify

Answer 1

\[(x^6y^4)^{1/8}+2(x^{1/3}y^{1/4})^2\]

Answer 2

I ended up with

\[2\sqrt{y}+\sqrt[8]{x^6}+\sqrt[3]{2x^2}\]

Answer 3

anyone wanna check for me?

Answer 4

First part:
\[\left( x^6y^4 \right)^{\frac{1}{8}} = x^{\frac{3}{4}} y^{\frac{1}{2}}\]
Second part:
\[2\left( x^{\frac{1}{3}} y^{\frac{1}{4}} \right)^2 = 2x^{\frac{2}{3}}y^{\frac{1}{2}}\]
Adding the two, we get
\[x^{\frac{3}{4}} y^{\frac{1}{2}} + 2x^{\frac{2}{3}}y^{\frac{1}{2}}\]
We can't combine the x terms because the exponents are different. We can, however, factor out the y term:
\[y^{\frac{1}{2}} \left( x^{\frac{3}{4}}+ 2x^{\frac{2}{3}} \right) \]

Answer 5

Oh right, I can't add the radicals from the parenthesis as it's multiplication

Answer 6

right

Answer 7

Right, that suggests multiplication. You can't change multiplication into addition.

Answer 8

is it more simplified to put them as radicals, though?