Solve 1/7*2^7-1/2*2^4+2

$$\frac{ 1 }{ 7 } \times { 2 }^{ 7 } - \frac{ 1 }{ 2 } \times { 2 }^{ 4 } +2$$

Evaluate

$$\frac{86}{7}\approx 12.285714286$$

Solution Steps

Calculate 2 to the power of 7 and get 128.

$$\frac{1}{7}\times 128-\frac{1}{2}\times 2^{4}+2$$

Multiply \frac{1}{7} and 128 to get \frac{128}{7}.

$$\frac{128}{7}-\frac{1}{2}\times 2^{4}+2$$

Calculate 2 to the power of 4 and get 16.

$$\frac{128}{7}-\frac{1}{2}\times 16+2$$

Multiply \frac{1}{2} and 16 to get \frac{16}{2}.

$$\frac{128}{7}-\frac{16}{2}+2$$

Divide 16 by 2 to get 8.

$$\frac{128}{7}-8+2$$

Convert 8 to fraction \frac{56}{7}.

$$\frac{128}{7}-\frac{56}{7}+2$$

Since \frac{128}{7} and \frac{56}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{128-56}{7}+2$$

Subtract 56 from 128 to get 72.

$$\frac{72}{7}+2$$

Convert 2 to fraction \frac{14}{7}.

$$\frac{72}{7}+\frac{14}{7}$$

Since \frac{72}{7} and \frac{14}{7} have the same denominator, add them by adding their numerators.

$$\frac{72+14}{7}$$

Add 72 and 14 to get 86.

$$\frac{86}{7}$$

Factor

$$\frac{2 \cdot 43}{7} = 12\frac{2}{7} = 12.285714285714286$$