Determining the larger of two sums having exponents

[Fogel]

Hello, I want to see if someone might be able to assist with a question.
I'm asked to determine which of two quantities is larger, or if they are equal:
2^30 -or- (2^29 + 2^29)
I'm even told that they are equal, but I'm uncertain how to work with (2^29 + 2^29) mathematically so that it equals 2^30.
I know it must be simple, but I don't know the "trick".

 

[Otis]

I'm even told that they are equal, but I'm uncertain how to work with (2^29 + 2^29) mathematically so that it equals 2^30

Hi Fogel. First Hints:

(4 + 4) = 2*4
(x + x) = 2*x
(a^m + a^m) = 2*a^m

 

[lev888]

Hello, I want to see if someone might be able to assist with a question.
I'm asked to determine which of two quantities is larger, or if they are equal:
2^30 -or- (2^29 + 2^29)
I'm even told that they are equal, but I'm uncertain how to work with (2^29 + 2^29) mathematically so that it equals 2^30.
I know it must be simple, but I don't know the "trick".

One approach I found useful is to simplify the problem so that the solution is almost obvious and then apply what you learned to the original problem.
So, how about 2^3 vs 2^2+2^2?

 

[Steven G]

You need to understand on your own that repeated addition can be expressed as multiplication, as Otis stated.

 

[Otis]

Second Hints:

b^m * b^n = b^(m + n)

For example:

b * b^n = b^(1 + n)