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

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

Evaluate

$$\frac{16}{455625}\approx 0.000035117$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

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

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

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

Calculate 6 to the power of 2 and get 36.

$$\frac{4}{625}\times \left(\frac{36}{2^{2}}\times \left(\frac{2}{3}\right)^{-1}\right)^{-2}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4}{625}\times \left(\frac{36}{4}\times \left(\frac{2}{3}\right)^{-1}\right)^{-2}$$

Divide 36 by 4 to get 9.

$$\frac{4}{625}\times \left(9\times \left(\frac{2}{3}\right)^{-1}\right)^{-2}$$

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

$$\frac{4}{625}\times \left(9\times \frac{3}{2}\right)^{-2}$$

Multiply 9 and \frac{3}{2} to get \frac{27}{2}.

$$\frac{4}{625}\times \left(\frac{27}{2}\right)^{-2}$$

Calculate \frac{27}{2} to the power of -2 and get \frac{4}{729}.

$$\frac{4}{625}\times \frac{4}{729}$$

Multiply \frac{4}{625} and \frac{4}{729} to get \frac{16}{455625}.

$$\frac{16}{455625}$$

Factor

$$\frac{2 ^ {4}}{3 ^ {6} \cdot 5 ^ {4}} = 3.511659807956104 \times 10^{-5}$$