Simplify the following algebraic expression and express your answer using positive exponents only. $\left( u ^ { - 1 } v ^ { - 2 } \right) ^ { 4 }$
A) $u ^ { 4 } v ^ { 8 }$
B) $\frac { 1 } { u ^ { 5 } v ^ { 6 } }$
C) $\frac { 1 } { u ^ { 4 } v ^ { 8 } }$
D) $u ^ { 5 } v ^ { 6 }$
E) $\frac { 1 } { u ^ { 3 } v ^ { 2 } }$

Question

Quizplus · Accepted Answer

To simplify the expression, we can use the property of exponents that says that when we raise a power to another power, we can multiply the exponents. Therefore,
$$\left(u^{-1}v^{-2}ight)^4=u^{-1	imes4}v^{-2	imes4}=u^{-4}v^{-8}=\frac{1}{u^4v^8}$$
So the answer is $\frac{1}{u^4v^8}$, which is option C when expressed with positive exponents.

Simplify the Following Algebraic Expression and Express Your Answer Using (u−1v−2)4\left( u ^ { - 1 } v ^ { - 2 } \right) ^ { 4 }(u−1v−2)4

Simplify the Following Algebraic Expression and Express Your Answer Using $\left( u ^ { - 1 } v ^ { - 2 } \right) ^ { 4 }$