Question

The value of $\frac{(5{)}^{0.25}\times (125{)}^{0.25}}{(256{)}^{0.10}\times (256{)}^{0.15}}$ is

• A. $\frac{\sqrt{5}}{2}$
• B. $\frac{5}{4}$
• C. $\frac{25}{2}$
• D. $\frac{25}{16}$

Answer 1

The correct option is B $\frac{5}{4}$

$\frac{{\left(5\right)}^{0.25}\times {\left(125\right)}^{0.25}}{{\left(256\right)}^{0.10}\times {\left(256\right)}^{0.15}}$
=$\frac{{\left(5\right)}^{0.25}\times {\left(5^3\right)}^{0.25}}{{\left(4^4\right)}^{0.10}\times {\left(4^4\right)}^{0.15}}$
=$\frac{{\left(5\right)}^{0.25}\times {\left(5\right)}^{0.75}}{{\left(4\right)}^{0.40}\times {\left(4\right)}^{0.60}}$
$=\frac{{\left(5\right)}^1}{{\left(4\right)}^1}=\frac{5}{4}$