Use the rules of exponents to simplify the expression $\left( 2 x ^ { 4 } y ^ { 6 } \right) ^ { - 2 }$ using only positive exponents. Assume that neither x nor y is 0.
A) $2 x ^ { 2 } y ^ { 4 }$
B) $\frac { 1 } { 4 x ^ { 8 } y ^ { 12 } }$
C) $\frac { 1 } { 2 x ^ { 8 } y ^ { 12 } }$
D) $4 x ^ { 2 } y ^ { 4 }$
E) $\frac { 2 } { x ^ { 8 } y ^ { 12 } }$

Question

Quizplus · Accepted Answer

To simplify the expression, we distribute the exponent of -2 to both the x and y terms inside the parentheses:
\begin{align*}
\left( 2 x ^ { 4 } y ^ { 6 } ight) ^ { - 2 } &= \frac{1}{\left( 2 x ^ { 4 } y ^ { 6 } ight) ^ {2}} \
&= \frac{1}{2^2 x ^ { 4 \cdot 2 } y ^ { 6 \cdot 2 }} \
&= \frac { 1 } { 4 x ^ { 8 } y ^ { 12 } }
\end{align*}
Therefore, the best choice is B.

Use the Rules of Exponents to Simplify the Expression (2x4y6)−2\left( 2 x ^ { 4 } y ^ { 6 } \right) ^ { - 2 }(2x4y6)−2

Use the Rules of Exponents to Simplify the Expression $\left( 2 x ^ { 4 } y ^ { 6 } \right) ^ { - 2 }$