Solve ((8-3/2)^2)^2-(5--7/3))^2

$$( ( 8 - \frac { 3 } { 2 } ) ^ { 2 } ) ^ { 2 } - ( 5 - \frac { - 7 } { 3 } ) ) ^ { 2 }$$

Evaluate

$$\frac{85331}{48}\approx 1777.729166667$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\left(8-\frac{3}{2}\right)^{4}-\left(5-\frac{-7}{3}\right)$$

Subtract \frac{3}{2} from 8 to get \frac{13}{2}.

$$\left(\frac{13}{2}\right)^{4}-\left(5-\frac{-7}{3}\right)$$

Calculate \frac{13}{2} to the power of 4 and get \frac{28561}{16}.

$$\frac{28561}{16}-\left(5-\frac{-7}{3}\right)$$

Fraction \frac{-7}{3} can be rewritten as -\frac{7}{3} by extracting the negative sign.

$$\frac{28561}{16}-\left(5-\left(-\frac{7}{3}\right)\right)$$

The opposite of -\frac{7}{3} is \frac{7}{3}.

$$\frac{28561}{16}-\left(5+\frac{7}{3}\right)$$

Add 5 and \frac{7}{3} to get \frac{22}{3}.

$$\frac{28561}{16}-\frac{22}{3}$$

Subtract \frac{22}{3} from \frac{28561}{16} to get \frac{85331}{48}.

$$\frac{85331}{48}$$

Factor

$$\frac{85331}{2 ^ {4} \cdot 3} = 1777\frac{35}{48} = 1777.7291666666667$$