Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent
positive real numbers.
-$$\left( 81 \mathrm { k } ^ { 4 } \mathrm {~m} ^ { - 8 } \right) ^ { 1 / 4 }$$
A) $\frac { 3 k } { m ^ { 2 } }$
B) $3 \mathrm {~km} ^ { 2 }$
C) $\frac { 4 k } { m ^ { 2 } }$
D) $4 \mathrm {~km} ^ { 2 }$

Question

Quizplus · Accepted Answer

Taking the fourth root of $81k^4m^{-8}$ simplifies to $\frac{3k}{m^2}$ because the fourth root of 81 is 3, the fourth root of $k^4$ is $k$, and the fourth root of $m^{-8}$ is $m^{-2}$, which can be written as $\frac{1}{m^2}$.

Perform the Indicated Operations (81k4 m−8)1/4\left( 81 \mathrm { k } ^ { 4 } \mathrm {~m} ^ { - 8 } \right) ^ { 1 / 4 }(81k4 m−8)1/4

Perform the Indicated Operations $\left( 81 \mathrm { k } ^ { 4 } \mathrm {~m} ^ { - 8 } \right) ^ { 1 / 4 }$