# Subtracting exponents properties?

Background : I was reviewing some practice problems for a small local math competition, and I don't understand how the give solution works.

I don't know how this, $$9^{x+2} - 9^x=240$$ is the same as this $$9^x(81-1)=240$$

I don't know if there is something simple I am missing, or if there is a property I have never learned that is being used in this solution. I have looked around for a solution but haven't found one that fits my needs, or at least I haven't figured out how to apply it to this problem.

• $9^{x+2} = 9^x \cdot 9^2 = 9^x \cdot 81$ Commented Jan 21, 2019 at 1:46
• Oh wow I overthought that WAY too much. Thank you
– Bill
Commented Jan 21, 2019 at 1:49

Will Jagy is correct, but to expand just a little bit take what he said and then let $$9^x=a$$. If we do that we get
$$81a-a=240$$.
From here we could just take one $$a$$ away and express $$80a=240$$, but the authors chose to express it as $$a(81-1)$$. If we replace $$a$$ with $$9^x$$ we have
$$9^x(81-1) = 240$$.