Solve (12-4/5)^-2+sqrt{25/16}-2^-1=

$$( 12 - \frac { 4 } { 5 } ) ^ { - 2 } + \sqrt { \frac { 25 } { 16 } } - 2 ^ { - 1 } =$$

Evaluate

$$\frac{2377}{3136}\approx 0.757971939$$

Solution Steps

Subtract \frac{4}{5} from 12 to get \frac{56}{5}.

$$\left(\frac{56}{5}\right)^{-2}+\sqrt{\frac{25}{16}}-2^{-1}$$

Calculate \frac{56}{5} to the power of -2 and get \frac{25}{3136}.

$$\frac{25}{3136}+\sqrt{\frac{25}{16}}-2^{-1}$$

Rewrite the square root of the division \frac{25}{16} as the division of square roots \frac{\sqrt{25}}{\sqrt{16}}. Take the square root of both numerator and denominator.

$$\frac{25}{3136}+\frac{5}{4}-2^{-1}$$

Add \frac{25}{3136} and \frac{5}{4} to get \frac{3945}{3136}.

$$\frac{3945}{3136}-2^{-1}$$

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

$$\frac{3945}{3136}-\frac{1}{2}$$

Subtract \frac{1}{2} from \frac{3945}{3136} to get \frac{2377}{3136}.

$$\frac{2377}{3136}$$

Factor

$$\frac{2377}{2 ^ {6} \cdot 7 ^ {2}} = 0.7579719387755102$$