Evaluate \(\frac{8^{\frac{1}{3}} \times 5^{\frac{2}{3}}}{10^{\frac{2}{3}}}\) = \(\frac{8^{\frac{1}{3}} \times 5^{\frac{2}{3}}}{10^{\frac{2}{3}}}\)
A. \(\frac{2}{5}\)
B. \(\frac{5}{3}\)
C. 3\(\sqrt{5}\)
D. 3\(\sqrt{2}\)
Correct Answer: D
Explanation
\(\frac{8^{\frac{1}{3}} \times 5^{\frac{3}{2}}}{\frac{2}{10^3}}\) = \(\frac{(2^3)^{\frac{1}{3}} \times 5^{\frac{3}{2}}}{(2 \times 5)^{\frac{2}{3}}}\)
= \(\frac{2 \times 5}{2^{\frac{2}{3}} \times 5^{\frac{3}{2}}}\)
= 21 - \(\frac{2}{3}\)
= 2\(\frac{1}{3}\)
= 3\(\sqrt{2}\)
