Solve ((2/5^{2})^{2}(frac{6^{3}}{2^2}*(2/3)^-1)^-2)^-1

$$( ( \frac { 2 } { 5 ^ { 2 } } ) ^ { 2 } ( \frac { 6 ^ { 3 } } { 2 ^ { 2 } } \cdot ( \frac { 2 } { 3 } ) ^ { - 1 } ) ^ { - 2 } ) ^ { - 1 }$$

Evaluate

$$\frac{4100625}{4}=1025156.25$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$\left(\left(\frac{2}{25}\right)^{2}\times \left(\frac{6^{3}}{2^{2}}\times \left(\frac{2}{3}\right)^{-1}\right)^{-2}\right)^{-1}$$

Calculate \frac{2}{25} to the power of 2 and get \frac{4}{625}.

$$\left(\frac{4}{625}\times \left(\frac{6^{3}}{2^{2}}\times \left(\frac{2}{3}\right)^{-1}\right)^{-2}\right)^{-1}$$

Calculate 6 to the power of 3 and get 216.

$$\left(\frac{4}{625}\times \left(\frac{216}{2^{2}}\times \left(\frac{2}{3}\right)^{-1}\right)^{-2}\right)^{-1}$$

Calculate 2 to the power of 2 and get 4.

$$\left(\frac{4}{625}\times \left(\frac{216}{4}\times \left(\frac{2}{3}\right)^{-1}\right)^{-2}\right)^{-1}$$

Divide 216 by 4 to get 54.

$$\left(\frac{4}{625}\times \left(54\times \left(\frac{2}{3}\right)^{-1}\right)^{-2}\right)^{-1}$$

Calculate \frac{2}{3} to the power of -1 and get \frac{3}{2}.

$$\left(\frac{4}{625}\times \left(54\times \frac{3}{2}\right)^{-2}\right)^{-1}$$

Multiply 54 and \frac{3}{2} to get 81.

$$\left(\frac{4}{625}\times 81^{-2}\right)^{-1}$$

Calculate 81 to the power of -2 and get \frac{1}{6561}.

$$\left(\frac{4}{625}\times \frac{1}{6561}\right)^{-1}$$

Multiply \frac{4}{625} and \frac{1}{6561} to get \frac{4}{4100625}.

$$\left(\frac{4}{4100625}\right)^{-1}$$

Calculate \frac{4}{4100625} to the power of -1 and get \frac{4100625}{4}.

$$\frac{4100625}{4}$$

Factor

$$\frac{3 ^ {8} \cdot 5 ^ {4}}{2 ^ {2}} = 1025156\frac{1}{4} = 1025156.25$$