Solve {[(1/5)^{-2}*5^{3}]^-1*(1/5)^-4}^2:(2/15)^2

$$\{ [ ( \frac { 1 } { 5 } ) ^ { - 2 } \cdot 5 ^ { 3 } ] ^ { - 1 } \cdot ( \frac { 1 } { 5 } ) ^ { - 4 } \} ^ { 2 } : ( \frac { 2 } { 15 } ) ^ { 2 }$$

Evaluate

$$\frac{9}{4}=2.25$$

Solution Steps

Calculate \frac{1}{5} to the power of -2 and get 25.

$$\frac{\left(\left(25\times 5^{3}\right)^{-1}\times \left(\frac{1}{5}\right)^{-4}\right)^{2}}{\left(\frac{2}{15}\right)^{2}}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{\left(\left(25\times 125\right)^{-1}\times \left(\frac{1}{5}\right)^{-4}\right)^{2}}{\left(\frac{2}{15}\right)^{2}}$$

Multiply 25 and 125 to get 3125.

$$\frac{\left(3125^{-1}\times \left(\frac{1}{5}\right)^{-4}\right)^{2}}{\left(\frac{2}{15}\right)^{2}}$$

Calculate 3125 to the power of -1 and get \frac{1}{3125}.

$$\frac{\left(\frac{1}{3125}\times \left(\frac{1}{5}\right)^{-4}\right)^{2}}{\left(\frac{2}{15}\right)^{2}}$$

Calculate \frac{1}{5} to the power of -4 and get 625.

$$\frac{\left(\frac{1}{3125}\times 625\right)^{2}}{\left(\frac{2}{15}\right)^{2}}$$

Multiply \frac{1}{3125} and 625 to get \frac{1}{5}.

$$\frac{\left(\frac{1}{5}\right)^{2}}{\left(\frac{2}{15}\right)^{2}}$$

Calculate \frac{1}{5} to the power of 2 and get \frac{1}{25}.

$$\frac{\frac{1}{25}}{\left(\frac{2}{15}\right)^{2}}$$

Calculate \frac{2}{15} to the power of 2 and get \frac{4}{225}.

$$\frac{\frac{1}{25}}{\frac{4}{225}}$$

Divide \frac{1}{25} by \frac{4}{225} by multiplying \frac{1}{25} by the reciprocal of \frac{4}{225}.

$$\frac{1}{25}\times \frac{225}{4}$$

Multiply \frac{1}{25} and \frac{225}{4} to get \frac{9}{4}.

$$\frac{9}{4}$$

Factor

$$\frac{3 ^ {2}}{2 ^ {2}} = 2\frac{1}{4} = 2.25$$