Simplify the following algebraic expression and express your answer using positive exponents only. $\left( a ^ { - 1 } v ^ { - 2 } \right) ^ { 7 }$
A) $a ^ { 8 } v ^ { 9 }$
B) $\frac { 1 } { a ^ { 8 } v ^ { 9 } }$
C) $\frac { 1 } { a ^ { 6 } v ^ { 5 } }$
D) $a ^ { 7 } v ^ { 14 }$
E) $\frac { 1 } { a ^ { 7 } v ^ { 14 } }$

Question

Quizplus · Accepted Answer

When raising a power to a power, multiply the exponents: $(a^{-1})^7 = a^{-7}$ and $(v^{-2})^7 = v^{-14}$. Thus, $(a^{-1}v^{-2})^7 = a^{-7}v^{-14}$. To express with positive exponents, take the reciprocal: $\frac{1}{a^7v^{14}}$.

Simplify the Following Algebraic Expression and Express Your Answer Using (a−1v−2)7\left( a ^ { - 1 } v ^ { - 2 } \right) ^ { 7 }(a−1v−2)7

Simplify the Following Algebraic Expression and Express Your Answer Using $\left( a ^ { - 1 } v ^ { - 2 } \right) ^ { 7 }$