Question 1100214
<br>
(a^2 b^8 c^5)^2(a^5 c^2)^3(a^-2 bc^-1)^3)   original expression<br>
(a^4 b^16 c^10) (a^15 c^6) (a^-6 b^3 c^-3)  using power of power rule<br>
(a^(4+15-6)) (b^(16+3)) (c^(10+6-3))        using multiplication of power rule<br>
(a^13) (b^19) (c^13)<br>
Answer C<br>
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.<br>
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.