Solve (73/4)^8-(81/4)^2

$$( 7 \frac { 3 } { 4 } ) ^ { 8 } - ( 8 \frac { 1 } { 4 } ) ^ { 2 }$$

Evaluate

$$\frac{852886576897}{65536}\approx 13014016.371109009$$

Solution Steps

Multiply 7 and 4 to get 28.

$$\left(\frac{28+3}{4}\right)^{8}-\left(\frac{8\times 4+1}{4}\right)^{2}$$

Add 28 and 3 to get 31.

$$\left(\frac{31}{4}\right)^{8}-\left(\frac{8\times 4+1}{4}\right)^{2}$$

Calculate \frac{31}{4} to the power of 8 and get \frac{852891037441}{65536}.

$$\frac{852891037441}{65536}-\left(\frac{8\times 4+1}{4}\right)^{2}$$

Multiply 8 and 4 to get 32.

$$\frac{852891037441}{65536}-\left(\frac{32+1}{4}\right)^{2}$$

Add 32 and 1 to get 33.

$$\frac{852891037441}{65536}-\left(\frac{33}{4}\right)^{2}$$

Calculate \frac{33}{4} to the power of 2 and get \frac{1089}{16}.

$$\frac{852891037441}{65536}-\frac{1089}{16}$$

Subtract \frac{1089}{16} from \frac{852891037441}{65536} to get \frac{852886576897}{65536}.

$$\frac{852886576897}{65536}$$

Factor

$$\frac{17 \cdot 54449 \cdot 921409}{2 ^ {16}} = 13014016\frac{24321}{65536} = 13014016.371109009$$