Solve (31/8)^2:25^2]:[4^2:(-16)^2]=

$$( 3 \frac { 1 } { 8 } ) ^ { 2 } : 25 ^ { 2 } ] : [ 4 ^ { 2 } : ( - 16 ) ^ { 2 } ] =$$

Evaluate

$$\frac{1}{64}=0.015625$$

Solution Steps

Multiply 3 and 8 to get 24.

$$\frac{\left(\frac{24+1}{8}\right)^{2}}{25^{2}}$$

Add 24 and 1 to get 25.

$$\frac{\left(\frac{25}{8}\right)^{2}}{25^{2}}$$

Calculate \frac{25}{8} to the power of 2 and get \frac{625}{64}.

$$\frac{\frac{625}{64}}{25^{2}}$$

Calculate 25 to the power of 2 and get 625.

$$\frac{\frac{625}{64}}{625}$$

Express \frac{\frac{625}{64}}{625} as a single fraction.

$$\frac{625}{64\times 625}$$

Cancel out 625 in both numerator and denominator.

$$\frac{1}{64}$$

Factor

$$\frac{1}{2 ^ {6}} = 0.015625$$