# Thread: EXPONENTS AND ROOTS What is the m root of (16^2m + 64^m) /(8^m + 32^m)?

1. ## EXPONENTS AND ROOTS What is the m root of (16^2m + 64^m) /(8^m + 32^m)?

Sorry, I'm not good with notations, if you can't understand this: the m root of (16^2m + 64^m) /(8^m + 32^m)

Here's an image of the equation:

The answer, according to the book, is 8, but, unfortunately, it doesn't show the solution. Can you show me why it's 8 please?

Thanks a lot!

2. ## Re: EXPONENTS AND ROOTS What is the m root of (16^2m + 64^m) /(8^m + 32^m)?

I'll get you started,

$\displaystyle \frac{16^{2m}+64^m}{8^m+32^m}$

$\displaystyle =\frac{(2^4)^{2m}+(2^6)^m}{(2^3)^m+(2^5)^m}$

$\displaystyle =\frac{2^{8m}+2^{6m}}{2^{3m}+2^{5m}}$

Now factorise..

3. ## Re: EXPONENTS AND ROOTS What is the m root of (16^2m + 64^m) /(8^m + 32^m)?

Originally Posted by a tutor
I'll get you started,

$\displaystyle \frac{16^{2m}+64^m}{8^m+32^m}$

$\displaystyle =\frac{(2^4)^{2m}+(2^6)^m}{(2^3)^m+(2^5)^m}$

$\displaystyle =\frac{2^{8m}+2^{6m}}{2^{3m}+2^{5m}}$

Now factorise..
Actually, that's where I get stuck. I can't get past that point, but good to know I was on the right track

4. ## Re: EXPONENTS AND ROOTS What is the m root of (16^2m + 64^m) /(8^m + 32^m)?

$\displaystyle =\frac{2^{8m}+2^{6m}}{2^{3m}+2^{5m}}$

$\displaystyle =\frac{2^{6m}(2^{2m}+1)}{2^{3m}(2^{2m}+1)}=2^{3m}$