# Math Help - Simplifying radicals

1. ## Simplifying radicals

Express/simplify as a single log
[(3/2)ln4x^6]-[(4/5)ln2y^10]

book answer is 2^(11/5)x^9/y^8
my answer is (8x^9)/[(16^1/5)y^8]

I need to simplify 8/[16^(1/5)] to get to 2^(11/5)/1 which equals 2^(11/5)x^9/y^8
I'm oblivious as to how this is achieved, please help.

2. ## Re: Simplifying radicals

Originally Posted by Greymalkin
Express/simplify as a single log
[(3/2)ln4x^6]-[(4/5)ln2y^10]

book answer is 2^(11/5)x^9/y^8
my answer is (8x^9)/[(16^1/5)y^8]

I need to simplify 8/[16^(1/5)] to get to 2^(11/5)/1 which equals 2^(11/5)x^9/y^8
I'm oblivious as to how this is achieved, please help.
8/{16^(1/5)}= 2^3/(2^4)^(1/5)=2^3/2^(4/5) =2^(3-4/5)=2^(11/5)

3. ## Re: Simplifying radicals

The book kept the 8 and 16 as powers of 2:

$\ln\frac{8x^9}{16^{1/5}y^8}$

$=\ln\frac{2^3x^9}{2^{4/5}y^8}$

$=\ln\frac{2^{3-4/5}x^9}{y^8}$

$=\ln\frac{2^{11/5}x^9}{y^8}$