SOLUTION: ((2x)^2)((4x)^4)((8x)^6)= a.) (2^22)(x^12) b.) (2^24)(x^12) c.) (2^26)(x^12)

Algebra ->  Exponents -> SOLUTION: ((2x)^2)((4x)^4)((8x)^6)= a.) (2^22)(x^12) b.) (2^24)(x^12) c.) (2^26)(x^12)       Log On


   

Question 84532: ((2x)^2)((4x)^4)((8x)^6)=
a.) (2^22)(x^12)
b.) (2^24)(x^12)
c.) (2^26)(x^12)
d.) (2^28)(x^12)
I know the answer is d. but how would you arrive at that answer without multiple choice answer. Say this was on a test and it wasn't multiple choice, how would you arrive at the correct answer in that format. I understand how to get the x^12 but I do not know how to arrive at 2^28. How do get from 268435456 to 2^28?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28%282x%29%5E2%29%28%284x%29%5E4%29%28%288x%29%5E6%29 Start with the given expression

%282%5E2x%5E2%29%284%5E4x%5E4%29%288%5E6x%5E6%29 Distribute the exponent

%282%5E2%2A4%5E4%2A8%5E6%29%28x%5E2x%5E4x%5E6%29 Group like terms

%282%5E2%2A%282%5E2%29%5E4%2A%282%5E3%29%5E6%29%28x%5E2x%5E4x%5E6%29 Rewrite the base 4 as 2%5E2 and 8 as 2%5E3

%282%5E2%2A2%5E%282%2A4%29%2A2%5E%283%2A6%29%29%28x%5E2x%5E4x%5E6%29 Multiply the exponents

%282%5E2%2A2%5E8%2A2%5E18%29%28x%5E2x%5E4x%5E6%29

%282%5E%282%2B8%2B18%29%29%28x%5E%282%2B4%2B6%29%29 Now that we have similar bases, add the exponents

%282%5E28%29%28x%5E12%29 So this is your answer