Find the Power of a Quotient
-$$\left( \frac { - 21 x ^ { 12 } y ^ { 6 } } { 7 x ^ { 17 } y ^ { - 2 } } \right) ^ { 3 }$$
A) $\frac { - 27 y ^ { 24 } } { x ^ { 15 } }$
B) $\frac { 27 y ^ { 24 } } { x ^ { 15 } }$
C) $\frac { - 27 y ^ { 12 } } { x ^ { 15 } }$
D) $\frac { - 27 } { x ^ { 15 } y ^ { 24 } }$

Question

Quizplus · Accepted Answer

First, simplify the fraction inside the parenthesis: $\frac{-21}{7} = -3$, and subtract the exponents for $x$ and $y$: $x^{12-17} = x^{-5}$, $y^{6-(-2)} = y^8$. Then, raise each part to the power of 3: $(-3)^3 = -27$, $x^{-5 \cdot 3} = x^{-15}$, $y^{8 \cdot 3} = y^{24}$. The result is $\frac{-27y^{24}}{x^{15}}$.

Find the Power of a Quotient - (−21x12y67x17y−2)3\left( \frac { - 21 x ^ { 12 } y ^ { 6 } } { 7 x ^ { 17 } y ^ { - 2 } } \right) ^ { 3 }(7x17y−2−21x12y6​)3

Find the Power of a Quotient
- $\left( \frac { - 21 x ^ { 12 } y ^ { 6 } } { 7 x ^ { 17 } y ^ { - 2 } } \right) ^ { 3 }$