Use the rules of exponents to simplify the expression $−2\left( 2 x ^ { 4 } y ^ { 6 } \right) ^ { - 2 }$ using only positive exponents. Assume that neither x nor y is 0.

A) $2 x ^ { 2 } y ^ { 4 }$
B) $14x8y12\frac { 1 } { 4 x ^ { 8 } y ^ { 12 } }$
C) $12x8y12\frac { 1 } { 2 x ^ { 8 } y ^ { 12 } }$
D) $4 x ^ { 2 } y ^ { 4 }$
E) $2x8y12\frac { 2 } { x ^ { 8 } y ^ { 12 } }$

Question

Use the rules of exponents to simplify the expression

−2\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)

14x8y12\frac { 1 } { 4 x ^ { 8 } y ^ { 12 } }

C)

12x8y12\frac { 1 } { 2 x ^ { 8 } y ^ { 12 } }

D)

4 x ^ { 2 } y ^ { 4 }

E)

2x8y12\frac { 2 } { x ^ { 8 } y ^ { 12 } }

Himanshu Ahlawat · Accepted Answer

Final Answer : B, Explanation :   To simplify the expression, we distribute the exponent of -2 to both the x and y terms inside the parentheses: ( 2 x 4 y 6 ) − 2 = 1 ( 2 x 4 y 6 ) 2 = 1 2 2 x 4 ⋅ 2 y 6 ⋅ 2 = 1 4 x 8 y 12  \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 } }  ( 2 x 4 y 6 ) − 2 ​ = ( 2 x 4 y 6 ) 2 1 ​ = 2 2 x 4 ⋅ 2 y 6 ⋅ 2 1 ​ = 4 x 8 y 12 1 ​ ​ Therefore, the best choice is B.

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