Question

The value of $(0.000064{)}^{\frac{5}{6}}÷(0.00032{)}^{\frac{6}{5}}$ is

• A. 0.2
• B. 5
• C. 0.4
• D. 2.5

Answer 1

Answer: (B)

$(0.000064{)}^{\frac{5}{6}}÷(0.00032{)}^{\frac{6}{5}}={\left((0.2{)}^6\right)}^{\frac{5}{6}}÷{\left((0.2{)}^5\right)}^{\frac{6}{5}}$
$=(0.2{)}^{6\times \frac{5}{6}}÷(0.2{)}^{5\times \frac{6}{5}}\left[\text{ As, }{\left(x^m\right)}^n=x^{mn}\right]$
$=(0.2{)}^5÷(0.2{)}^6$
$=(0.2{)}^{5-6}\left[\text{ As, }{x}^m÷x^n=x^{m-n}\right]$
$=(0.2{)}^{-1}=\frac{1}{0.2}=\frac{10}{2}=5$