1. ## help with radical exponents

$\displaystyle 3 root (x ^2 y ^ 5) ^ 12$ how do i write that as a single radical expression?

2. Originally Posted by diehardmath4
$\displaystyle 3 root (x ^2 y ^ 5) ^ 12$ how do i write that as a single radical expression?

Hello diehardmath4,

$\displaystyle \sqrt[3]{(x^2y^5)^{12}}=(x^2y^5)^4=x^8y^{20}$

3. can you please explain it a little further because i'm having a bit of trouble breaking down the steps

4. Originally Posted by diehardmath4
can you please explain it a little further because i'm having a bit of trouble breaking down the steps

$\displaystyle \sqrt[3]{(x^2y^5)^{12}}=(x^2y^5)^{\frac{12}{3}}=(x^2y^5)^4 =x^8y^{20}$

Recall this:

$\displaystyle \sqrt[n]{a^m}=a^{\frac{m}{n}}$

And maybe this, too:

$\displaystyle (x^ay^b)^n=x^{an}y^{bn}$

x ^ 8 / 15 y 7 / 15
__________________
x^1/3 y ^ - 1 / 5

I got x ^ 3 y 8 is that correct ?

6. Originally Posted by diehardmath4
x ^ 8 / 15 y 7 / 15
__________________
x^1/3 y ^ - 1 / 5

I got x ^ 3 y 8 is that correct ?
Actually, I got something different when I subtracted your exponents:

$\displaystyle \frac{8}{15}-\frac{1}{3}=\frac{1}{5}$

$\displaystyle \frac{7}{15}-\frac{-1}{5}=\frac{2}{3}$

$\displaystyle \dfrac{x^{\frac{8}{15}}y^{\frac{7}{15}}}{x^{\frac{ 1}{3}}y^{-\frac{1}{5}}}=x^{\frac{1}{3}}y^{\frac{2}{3}}$