Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers.
-$\left(243 \mathrm{k}^{5} \mathrm{~m}^{-10}\right)^{1 / 5}$

A) $\frac{5 \mathrm{k}}{\mathrm{m}^{2}}$

B) $3 \mathrm{~km}^{2}$

C) $5 \mathrm{~km}^{2}$

D) $\frac{3 \mathrm{k}}{\mathrm{m}^{2}}$

Question

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers.
-$\left(243 \mathrm{k}^{5} \mathrm{~m}^{-10}\right)^{1 / 5}$

A) $\frac{5 \mathrm{k}}{\mathrm{m}^{2}}$

B) $3 \mathrm{~km}^{2}$

C) $5 \mathrm{~km}^{2}$

D) $\frac{3 \mathrm{k}}{\mathrm{m}^{2}}$

Quizplus · Accepted Answer

The expression simplifies to $\frac{3 \mathrm{k}}{\mathrm{m}^{2}}$ by applying the fifth root to both the coefficient and the variables, where $243^{1/5} = 3$, $k^{5 \cdot 1/5} = k$, and $m^{-10 \cdot 1/5} = m^{-2}$.

Use the Rules of Exponents to Simplify the Expression (243k5 m−10)1/5\left(243 \mathrm{k}^{5} \mathrm{~m}^{-10}\right)^{1 / 5}(243k5 m−10)1/5

Use the Rules of Exponents to Simplify the Expression $\left(243 \mathrm{k}^{5} \mathrm{~m}^{-10}\right)^{1 / 5}$