Question

is there any trick I can use to solve the question below without expanding:

2^3 + 2^4

Answer 1

2^3 + 2^4
= 8 + 16
= 24

Don't know how much simpler we can make it.

How were you going to "expand" it?

Answer 2

Like there are rules for multipling eponents with the same base, I was wondering if there were rules for addition. If I were to get some complicated like:

3^-2/3 + 3^5/8

... it would take a longer time to solve.

Answer 3

no
If the bases are different, you cannot add or subtract them

e.g. x^3 + y^2 stays that way

If the bases are the same in addition, you can usually factor.

e.g. x^5 + x^2 = x^2(x^3 + 1)

Answer 4

Thank you :)