How do you add exponents of like bases? GMAT?

Question

I took a practice GMAT today and one of the questions is driving me out of my head.

2(3) + 2(3) + 2(3) + 3(3) + 3(3)

The numbers in parenthesis are the exponents.

If some one knows that answer, I hope I can ask about another

Answer 1

With all due respect to the other answerer's, she asked for the rule for adding exponents with like bases.

I'll write 2 raised to the 4th power as 2^4 (a more common notation).

I'm thinking that you may have written the problem down wrong -- otherwise the problem is just math and the exponents don't really simplify well.

2^3 + 2^3 + 3^3 + 3^3 + 3^3 can be written as:

2 x (2^3) + 3 x (3^3)

2 x (2^3) = 2 x (2 x 2 x 2) = 2^4
3 x (3^3) = 3 x (3 x 3 x 3) = 3^4

Answer 2

2^3 = 2 x 2 x 2 = 8
3^3 = 3 x 3 x 3 = 27
So 8+8+8 + 27 + 27 = 78

Answer 3

Adding Like Exponents

Answer 4

you cannot add exponents with like bases
Let x = 2^3 and y = 3^3
Then 2^3 + 2^3 + 2^3 + 3^3 + 3^3
is like x+x+x+y+y
3x+2y
where we know x = 2^3 and y = 3^3
3 * 2^3 + 2 * 3^3

*means times and ^ means exponent

OR just think of 2^3 + 2^3 + 2^3 as having three of them===>
3 * 2^3

Does your answer choice look like this?

Otherwise just do the math:
2^3 = 2*2*2 = 8
3^3 = 3*3*3 = 27
8+8+8+27+27
= 78 (does you ranswer choices look like that?)

Answer 5

The sum equals 3*2^3+2*3^2
Numerically, the answer would be 3*8+2*9=42

Answer 6

25^x + 5^x = 12 or { 5^2}^x + 5^x = 12 or 5^2x + 5^x- 12 =0 [ let 5^x = a ] so a^2 + a - 12 =0 or ( a- 3) ( a+4) =0 so a= 3 & a= - 4 so 5^x= 3 & 5^x = - 4 so xlog5 =log3 & xlog5 = log(-4) invalid so x= log3/log5 = 0.6826 ANSWER