Evaluate \(\frac{8^{\frac{1}{3}} \times 5^{\frac{2}{3}}}{10^{\frac{2}{3}}}\)
A
\(\frac{2}{5}\)
B
\(\frac{5}{3}\)
C
3\(\sqrt{5}\)
D
3\(\sqrt{2}\)
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
\(\frac{8^{\frac{1}{3}} \times 5^{\frac{2}{3}}}{10^{\frac{2}{3}}}\) = \(\frac{(2^3)^{\frac{1}{3}} \times 5^{\frac{2}{3}}}{(2 \times 5)^{\frac{2}{3}}}\)
= \(\frac{2 \times 5^{\frac{2}{3}}}{2^{\frac{2}{3}} \times 5^{\frac{2}{3}}}\)
= \(2^{1 - \frac{2}{3}}\) x \(5^{\frac{2}{3} - \frac{2}{3}}\)
= \(2^{\frac{1}{3}}\) x \(5^0\)
= \(\sqrt[3]{2}\)
Source: Myschool Past Questions Archive (Record #31698)