intermediate algrebra square roots

[LamamideAda25]

I need help simplifying this problem.


cubed root of x to the 22nd power y to the 7th power

I though it might not be able to be simplified

 

[masters]

I need help simplifying this problem.


cubed root of x to the 22nd power y to the 7th power

I though it might not be able to be simplified

Hi LamamideAda25,

$\displaystyle \sqrt[3]{x^{22}y^7}$

We can use a little modular arithmetic and do this quite simply.

Let's divide the exponents under the radical by the index 3.

First $\displaystyle \frac{22}{3}=7$ with a remainder of 1. We take 7 factors of x out of the radical and leave 1 factor inside.

$\displaystyle x^7\sqrt[3]{xy^7}$

Now, do the same for the 7.

$\displaystyle \frac{7}{3}=2$ remainder 1. We take 2 factors of y out of the radical and leave 1 factor inside.

$\displaystyle \boxed{\sqrt[3]{x^{22}y^7}=x^7y^2 \sqrt[3]{xy}}$

Apologies to m4bot.