Problem Solving

Could someone explain to me why the correct answer to this question is what it is? I can't find the fast and hard rule and my fried brain can't seem to work it out. Much appreciated!

Which of the following is equal to 2^5 + 2^5 + 3^5 + 3^5 + 3^5?

A) 5^6

B) 13^5

C) 2^6 + 3^6

D) 2^7 + 3^8

E) 4^5 + 9^5

simplify, simplify. I need to get that into my head.

2^5 + 2^5 = 2^5(1+1) = 2^5(2)

3^5 + 3^5 + 3^5 = 3^5(1+1+1) = 3^5(3)

answer is (of course) C

2^6 + 3^6

To solve this simple algebra, i will be explaining 2 approach to you. just be calm and let your mind be settle.
(a) for the first approach, this is a simple mathematics question you were exposed you during your fundamental education. it involves the direct approach by solving the question directly
2^5 + 2^5 + 3^5 + 3^5 + 3^5?
2^5=32
3^5=243
=32+32+243+243+243
=793
Have a look at the options available, using try and error, you will realize only option appeared simple at sight. on solving it,
2^6=64
3^6=729
then 2^6 + 3^6 =793
we actually worked out the question and answer simultaneously and see the one that give the same result. you must be very fast and able to convince yourself from the point you see an option and you noticed the result cannot come near their expectation. discard and move to the next option.

(b) Solving using the prime number solution approach, 2,3 and 5 are all prime number
2^5 + 2^5 + 3^5 + 3^5 + 3^5
on collecting the like term
2^5*(1+1) + 3^5 *(1+1+1)
2^5*(2^1) + 3^5 *(3^1)
2 ^(5+1) + 3^(5+1)
2^6 + 3^6
Now we have arrived at our right option which C.

Think of it this way:

x + x + x + y + y is 3x's and 2y's

If we've got two 2�s and three 3�s, then we've got

2*2� + 3*3�

and from there we're set!