Simplify. Write the answer using positive exponents only.
-$\left( 5 x ^ { 6 } y ^ { 6 } \right) ^ { 2 } \left( x ^ { 8 } y ^ { 1 } \right) ^ { - 3 }$
A) $\frac { 25 } { x ^ { 12 } y ^ { 9 } }$
B) $\frac { \mathrm { y } ^ { 9 } } { 25 \mathrm { x } ^ { 12 } }$
C) $25 x ^ { 12 } y ^ { 9 }$
D) $\frac { 25 y ^ { 9 } } { x ^ { 12 } }$

Question

Quizplus · Accepted Answer

To simplify the expression, apply the power of a product rule and the power of a power rule. For the first part, $(5x^6y^6)^2 = 25x^{12}y^{12}$. For the second part, $(x^8y)^{-3} = x^{-24}y^{-3}$. Multiplying these together gives $25x^{12-24}y^{12-3} = 25x^{-12}y^9$, which simplifies to $\frac{25y^9}{x^{12}}$.

Simplify Write the Answer Using Positive Exponents Only (5x6y6)2(x8y1)−3\left( 5 x ^ { 6 } y ^ { 6 } \right) ^ { 2 } \left( x ^ { 8 } y ^ { 1 } \right) ^ { - 3 }(5x6y6)2(x8y1)−3

Simplify Write the Answer Using Positive Exponents Only $\left( 5 x ^ { 6 } y ^ { 6 } \right) ^ { 2 } \left( x ^ { 8 } y ^ { 1 } \right) ^ { - 3 }$