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  4. The value of (0.000064)(5/6) ÷(0.00032)(6/5) is

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

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Solution:

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