Solve (2^4)^8/2^83-1/4

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

Evaluate

$$\frac{67108861}{12}\approx 5592405.083333333$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 4 and 8 to get 32.

$$\frac{2^{32}}{2^{8}\times 3}-\frac{1}{4}$$

Cancel out 2^{8} in both numerator and denominator.

$$\frac{2^{24}}{3}-\frac{1}{4}$$

Calculate 2 to the power of 24 and get 16777216.

$$\frac{16777216}{3}-\frac{1}{4}$$

Subtract \frac{1}{4} from \frac{16777216}{3} to get \frac{67108861}{12}.

$$\frac{67108861}{12}$$

Factor

$$\frac{37 \cdot 349 \cdot 5197}{2 ^ {2} \cdot 3} = 5592405\frac{1}{12} = 5592405.083333333$$