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.