Question

The value of $\frac{{\left(25\right)}^{5/2}\times {\left(243\right)}^{2/5}}{{\left(16\right)}^{3/4}\times {\left(8\right)}^{5/3}}$ is

• A. $\frac{5625}{128}$
• B. $\frac{5615}{256}$
• C. $\frac{5625}{256}$
• D. None

Answer 1

The correct option is D None

$\frac{{\left(25\right)}^{\frac{5}{2}}\times ({243)}^{\frac{2}{5}}}{{\left(16\right)}^{\frac{3}{4}}\times {\left(8\right)}^{\frac{5}{3}}}=\frac{5^5\times 3^2}{2^3\times 2^5}=\frac{3125\times 9}{8\times 32}=\frac{28125}{256}.$