Simplify. Assume all variables represent positive real numbers.
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Question

Quizplus · Accepted Answer

When we simplify the expression, we notice that each term has a common factor of $3b^2$. Factoring that out, we get $3b^2(4ac+9ab+8bc)$. Now, we can use the distributive property to factor out $3ab$ from the remaining terms in the expression, leaving us with $3b^2(3ab+4c)$. This expression cannot be simplified any further, so the answer is $\boxed{	extbf{(B) }11ebb63d\_1bfe\_1a33\_b851\_41c8228b098f\_TB8475\_11}$. We can simplify the given expression using the laws of exponents:
$$\frac{\sqrt{200}}{\sqrt{50}}\cdot\frac{\sqrt[3]{50}}{\sqrt[3]{10}}\cdot\frac{\sqrt{3}}{\sqrt{3}}\cdot\sqrt[6]{64}$$
$$=\frac{\sqrt{2\cdot100}}{\sqrt{2\cdot25}}\cdot\frac{\sqrt[3]{5^2}}{\sqrt[3]{2\cdot5}}\cdot\sqrt[6]{2^6}\cdot\sqrt{3}$$
$$=\frac{\sqrt{2}\cdot\sqrt{2}\cdot\sqrt{5^2}}{\sqrt{2}\cdot\sqrt{5}\cdot\sqrt{5}}\cdot\frac{\sqrt[3]{5^2}}{\sqrt[3]{2}\cdot\sqrt[3]{5}}\cdot2\cdot\sqrt{3}$$
$$=\frac{5}{5}\cdot\frac{\sqrt{5^2}}{\sqrt{2^2}}\cdot\frac{5}{2\cdot\sqrt[3]{5^2}}\cdot 2\cdot \sqrt{3}$$
$$=1\cdot\frac{5}{2}\cdot\frac{1}{\sqrt[3]{5^2}}\cdot 2\cdot\sqrt{3}$$
$$=\frac{5\sqrt{3}}{\sqrt[3]{25}}$$
$$=\frac{5\sqrt{3}\cdot\sqrt[3]{5^2}}{5}$$
$$=\sqrt{3}\cdot5^{\frac{2}{3}}$$
Therefore, the answer is $\boxed{	ext{(B) 11ebb63d_1bfe_1a33_b851_41c8228b098f_TB8475_11}}$.

Simplify. Assume All Variables Represent Positive Real Numbers