SOLUTION: what is the expended form of 2(a^2b^3c)^2 a. 4aaaabbbbcc b. 2aaaabbbbbcccc c. 4aaaabbbbbccc d. 2aaaabbbbbbcc

Algebra ->  Algebra  -> Exponential-and-logarithmic-functions -> SOLUTION: what is the expended form of 2(a^2b^3c)^2 a. 4aaaabbbbcc b. 2aaaabbbbbcccc c. 4aaaabbbbbccc d. 2aaaabbbbbbcc      Log On

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Question 86545: what is the expended form of 2(a^2b^3c)^2
a. 4aaaabbbbcc
b. 2aaaabbbbbcccc
c. 4aaaabbbbbccc
d. 2aaaabbbbbbcc
Answer by jim_thompson5910(28715) About Me  (Show Source):
You can put this solution on YOUR website!
2%28a%5E2b%5E3c%29%5E2

2%28a%5E2b%5E3c%29%28a%5E2b%5E3c%29 Expand
Start with the given expression

2%28a%5E2b%5E3c%29%28a%5E2b%5E3c%29

When you multiply common bases with exponents, you add the exponents


2a%5E%282%2B2%29b%5E%283%2B3%29c%5E%281%2B1%29 Add the exponents (note: the variables and exponents of the 2nd parenthesis now equal 1. So we don't need to bother with writing them out)

2a%5E4b%5E6c%5E2

So the expression

2%28a%5E2b%5E3c%29%5E2

simplifies to

2a%5E4b%5E6c%5E2

which really looks like

2aaaabbbbbbcc note: there are 4 a's, 6 b's, and 2 c's

so the answer is d)