evansbd wrote:The solution provided seems simple...but can someone explain the math?

Are the exponents being multiplied or is there more factoring not shown in the solution.


2(2^5) + 3(3^5)

I see that 2^5 = 32, so 2(2^5) = 64, which is 2^6.
I would have picked the correct answer because the others do not have the same first term on a real GMAT but what about factoring or doing the math of 3^5 or something similar w/o a calculator.

There are (at least) two ways to see why the answer is correct. We can factor:

2^5 + 2^5 + 3^5 + 3^5 + 3^5 = 2^5(1+1) + 3^5(1+1+1) = 2*2^5 + 3*3^5 = 2^6 + 3^6

Or we can understand that when we add something to itself, this is exactly what it means to multiply something by 2: x+x = 2x. Thus 2^5 + 2^5 = 2*2^5 = 2^6. And if you add something to itself three times, that's the same as multiplying by 3: x+x+x = 3x, so 3^5 + 3^5 + 3^5 = 3*3^5 = 3^6.