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?

Question

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?

callisto · Answer

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

callisto · Answer

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

callisto · Answer

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.

anonymous · Answer

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

callisto · Answer

:O
You're welcome!

anonymous · Answer

the answer is a^3b^4

anonymous · Answer

if it's a fraction you just deduct the exponent of the numerator to the exponent of the denominator..