Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers.
-$$\left( \frac { - 6 x ^ { 6 } y ^ { 5 } } { 3 x ^ { 12 } y ^ { - 2 } } \right) ^ { 3 }$$
A) $\frac { - 8 } { x ^ { 18 } y ^ { 21 } }$
B) $\frac { - 8 y ^ { 21 } } { x ^ { 18 } }$
C) $\frac { 8 y ^ { 21 } } { x ^ { 18 } }$
D) $\frac { - 8 y ^ { 9 } } { x ^ { 18 } }$

Question

Quizplus · Accepted Answer

First, simplify the fraction inside the parentheses by dividing the coefficients and subtracting the exponents: $(-2x^{-6}y^7)^3$. Then, apply the power of a power rule by multiplying the exponents: $-8y^{21}/x^{18}$.

Use the Laws of Exponents to Simplify Each Expression Using (−6x6y53x12y−2)3\left( \frac { - 6 x ^ { 6 } y ^ { 5 } } { 3 x ^ { 12 } y ^ { - 2 } } \right) ^ { 3 }(3x12y−2−6x6y5​)3

Use the Laws of Exponents to Simplify Each Expression Using $\left( \frac { - 6 x ^ { 6 } y ^ { 5 } } { 3 x ^ { 12 } y ^ { - 2 } } \right) ^ { 3 }$