Express the radical in simplified form.Assume that all variables represent positive real numbers.
-$\sqrt[3]{-27 a^{8} b^{5}}$
A) $3 a b \sqrt[3]{a^{3} b^{3}}$
B) $3 a b \sqrt[3]{a^{2} b^{2}}$
C) $3 \sqrt[3]{a^{2} b^{2}}$
D) $-3 a^{2} b \sqrt[3]{a^{2} b^{2}}$

Question

Quizplus · Accepted Answer

The expression $\sqrt[3]{-27 a^{8} b^{5}}$ simplifies to $-3 a^{2} b \sqrt[3]{a^{2} b^{2}}$ because $-27$ is the cube of $-3$, $a^{8}$ can be expressed as $a^{6} \cdot a^{2}$ where $a^{6}$ is the cube of $a^{2}$, and $b^{5}$ can be expressed as $b^{3} \cdot b^{2}$ where $b^{3}$ is the cube of $b$. Thus, taking the cube root of each part gives $-3 a^{2} b \sqrt[3]{a^{2} b^{2}}$.

Express the Radical in Simplified Form −27a8b53\sqrt[3]{-27 a^{8} b^{5}}3−27a8b5​ A) 3aba3b333 a b \sqrt[3]{a^{3} b^{3}}3ab3a3b3​

Express the Radical in Simplified Form $\sqrt[3]{-27 a^{8} b^{5}}$ A) $3 a b \sqrt[3]{a^{3} b^{3}}$