which expression is equivalent to $sqrt3{64a^{6}b^{7}c^{9}}$?\n$2abc^{2}(sqrt3{4a^{2}b^{3}c})$\n$4a^{2}b^{2}c…

which expression is equivalent to $sqrt3{64a^{6}b^{7}c^{9}}$?\n$2abc^{2}(sqrt3{4a^{2}b^{3}c})$\n$4a^{2}b^{2}c^{3}(sqrt3{b})$\n$8a^{3}b^{3}c^{4}(sqrt3{bc})$\n$8a^{2}b^{2}c^{3}(sqrt3{b})$

which expression is equivalent to $sqrt3{64a^{6}b^{7}c^{9}}$?\n$2abc^{2}(sqrt3{4a^{2}b^{3}c})$\n$4a^{2}b^{2}c^{3}(sqrt3{b})$\n$8a^{3}b^{3}c^{4}(sqrt3{bc})$\n$8a^{2}b^{2}c^{3}(sqrt3{b})$

Answer

Explanation:

Step1: Simplify cube - root of 64

The cube - root of 64 is 4 since $4^3=64$. So, $\sqrt[3]{64a^{6}b^{7}c^{9}}=\sqrt[3]{64}\cdot\sqrt[3]{a^{6}}\cdot\sqrt[3]{b^{7}}\cdot\sqrt[3]{c^{9}} = 4\sqrt[3]{a^{6}}\cdot\sqrt[3]{b^{7}}\cdot\sqrt[3]{c^{9}}$.

Step2: Simplify $\sqrt[3]{a^{6}}$

Using the rule $\sqrt[n]{x^{m}}=x^{\frac{m}{n}}$, we have $\sqrt[3]{a^{6}}=a^{\frac{6}{3}} = a^{2}$.

Step3: Simplify $\sqrt[3]{b^{7}}$

$\sqrt[3]{b^{7}}=\sqrt[3]{b^{6}\cdot b}=b^{2}\sqrt[3]{b}$.

Step4: Simplify $\sqrt[3]{c^{9}}$

$\sqrt[3]{c^{9}}=c^{\frac{9}{3}} = c^{3}$.

Step5: Combine the simplified terms

$4\sqrt[3]{a^{6}}\cdot\sqrt[3]{b^{7}}\cdot\sqrt[3]{c^{9}}=4\cdot a^{2}\cdot b^{2}\sqrt[3]{b}\cdot c^{3}=4a^{2}b^{2}c^{3}\sqrt[3]{b}$.

Answer:

$4a^{2}b^{2}c^{3}\left(\sqrt[3]{b}\right)$