Question

 216^{ \frac{-1}{3} } *  (\frac{1}{6})^{-2}-  5^{-1}*( \frac{1}{25})^{ \frac{-1}{2} }   

Answer 1

$216^{- \frac{1}{3} } \cdot (\frac{1}{6})^{-2}- 5^{-1}\cdot( \frac{1}{25})^{- \frac{1}{2} } = \\\ = \frac{1}{ \sqrt[3]{216} } \cdot 6^2- \frac{1}{5} \cdot \sqrt{25} = \frac{1}{ 6 } \cdot 36- 0,2 \cdot 5 =6-1=5$

Answer 2

Let's simplify the expression step by step:

First, we can simplify the exponent of the first term:

$216^{ \frac{-1}{3} } = \frac{1}{216^{\frac{1}{3}}} = \frac{1}{6}$

Next, we can simplify the exponent of the second term:

$(\frac{1}{6})^{-2} = \frac{1}{(\frac{1}{6})^2} = \frac{1}{\frac{1}{36}} = 36$

Then, we can simplify the second term:

$5^{-1}( \frac{1}{25})^{ \frac{-1}{2} } = \frac{1}{5}\frac{1}{\sqrt{\frac{1}{25}}} = \frac{1}{5} * \frac{1}{\frac{1}{5}} = 1$

Now, we can substitute the simplified values into the original expression:

$\frac{1}{6} * 36 - 1 = 6 - 1 = 5$

Therefore, the final answer is 5.