Simplify $a b ^ { 3 } c ^ { 2 } \left( \frac { 2 a ^ { 2 } b } { c ^ { 4 } } \right) ^ { - 1 }$ and eliminate any negative exponents.
A)
$b ^ { 2 } c ^ { 6 }$
B)
$\frac { b ^ { 6 } c ^ { 2 } } { 2 a ^ { 2 } }$
C)
$\frac { 2 b ^ { 2 } c ^ { 6 } } { 3 a }$
D)
$\frac { b ^ { 2 } c ^ { 6 } } { 2 a }$
E)
$2 b ^ { 2 } c ^ { 6 }$

Question

Simplify $a b ^ { 3 } c ^ { 2 } \left( \frac { 2 a ^ { 2 } b } { c ^ { 4 } } \right) ^ { - 1 }$ and eliminate any negative exponents. 
A)
 $b ^ { 2 } c ^ { 6 }$ 
B)
 $\frac { b ^ { 6 } c ^ { 2 } } { 2 a ^ { 2 } }$ 
C)
 $\frac { 2 b ^ { 2 } c ^ { 6 } } { 3 a }$ 
D)
 $\frac { b ^ { 2 } c ^ { 6 } } { 2 a }$ 
E)
 $2 b ^ { 2 } c ^ { 6 }$

Quizplus · Accepted Answer

To simplify $a b ^ { 3 } c ^ { 2 } \left( \frac { 2 a ^ { 2 } b } { c ^ { 4 } } \right) ^ { - 1 }$, we first distribute the exponent of -1 to the terms inside the parentheses, which flips the fraction and changes the signs of the exponents. This gives us $a b^3 c^2 \cdot \frac{c^4}{2a^2b}$. Simplifying this expression by canceling and combining like terms, we get $\frac{b^2 c^6}{2a}$.

Simplify ab3c2(2a2bc4)−1a b ^ { 3 } c ^ { 2 } \left( \frac { 2 a ^ { 2 } b } { c ^ { 4 } } \right) ^ { - 1 }ab3c2(c42a2b​)−1

Simplify $a b ^ { 3 } c ^ { 2 } \left( \frac { 2 a ^ { 2 } b } { c ^ { 4 } } \right) ^ { - 1 }$