## anonymous 3 years ago Simplify: a^7 b^8 /a^4b^4 Would the answer be a11/b12? For some reason, I had the idea that you were always supposed to add the exponents. But since this is division would you subtract the exponents instead?

1. Callisto

$\frac{x^a}{x^b}=x^{a-b}$

2. Callisto

Reason: $x^a \cdot x^b = x^{a+b}$$\frac{1}{x^b} = x^{-b}$ So, $\frac{x^a}{x^b} = x^a \frac{1}{x^b} = x^{a} \cdot x^{-b}=x^{a+(-b)}=x^{a-b}$

3. Callisto

For the answers to your questions, it is not a^11 / b^12. When it is division, you will do subtraction for the power of the same base.

4. anonymous

Thanks for explaining it - I was trying to write it all down! :)

5. Callisto

:O You're welcome!

6. anonymous