Question

$(\frac{125}{8})^{2/3}(\frac{16}{625})^{1/2}=$

• A. 1
• B. 4
• C. 8
• D. 25

Answer 1

Answer:

A. 1

$(\frac{125}{8})^{2/3}(\frac{16}{625})^{1/2}$

$=(\frac{5^3}{2^3})^{2/3}(\frac{4^2}{25^2})^{1/2}$

$=(\frac52)^{3\times{2/3}}\times(\frac{4}{25})^{2\times{1/2}}$

$=\frac{25}{4}\times\frac{4}{25}$

$=1$