Question 1100214: Simplify the expression below: (a^2 b^8 c^5)^2(a^5 c^2)^3(a^-2 bc^-1)^3)
A. 6(a^8 b^12 c^4)
B. a^21 b^24 c^10
C. a^13 b^19 c^13
D. a^21 b^29 c^14
Answer by greenestamps(13209)   (Show Source):
You can put this solution on YOUR website!
(a^2 b^8 c^5)^2(a^5 c^2)^3(a^-2 bc^-1)^3) original expression
(a^4 b^16 c^10) (a^15 c^6) (a^-6 b^3 c^-3) using power of power rule
(a^(4+15-6)) (b^(16+3)) (c^(10+6-3)) using multiplication of power rule
(a^13) (b^19) (c^13)
Answer C
Note: If this is a multiple choice question on a test, there is no need to simplify the entire expression. In the answer choices, the powers of b and c are all different. So just determine the power of either b or c in the simplified expression.
For example, suppose you look only at variable b. You have (b^16)*(b^3) = b^19; answer C is the only one with the correct exponent on b.
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