Question

The value of $\frac{(2{)}^{0.25}\times (8{)}^{0.25}}{(81{)}^{0.10}\times (81{)}^{0.15}}$ is---

• A. $\frac{3}{2}$
• B. $\frac{2}{3}$
• C. $\frac{\sqrt{2}}{3}$
• D. $\frac{4}{9}$

Answer 1

Answer: (B)

$\frac{2}{3}$

$\frac{(2{)}^{0.25}\times (8{)}^{0.25}}{(81{)}^{0.10}\times (81{)}^{0.15}}$

= $\frac{(2{)}^{0.25}\times (2^3{)}^{0.25}}{(3^4{)}^{0.10}\times (3^4{)}^{0.15}}$

= $\frac{(2{)}^{0.25}\times (2{)}^{0.75}}{(3{)}^{0.40}\times (3{)}^{0.60}}$

= $\frac{2^1}{3^1}=\frac{2}{3}$