Solve 8(1/16)^2-(1/16)^4=

$$8 ( \frac { 1 } { 16 } ) ^ { 2 } - ( \frac { 1 } { 16 } ) ^ { 4 } =$$

Evaluate

$$\frac{2047}{65536}=0.031234741$$

Solution Steps

Calculate \frac{1}{16} to the power of 2 and get \frac{1}{256}.

$$8\times \frac{1}{256}-\left(\frac{1}{16}\right)^{4}$$

Multiply 8 and \frac{1}{256} to get \frac{8}{256}.

$$\frac{8}{256}-\left(\frac{1}{16}\right)^{4}$$

Reduce the fraction \frac{8}{256} to lowest terms by extracting and canceling out 8.

$$\frac{1}{32}-\left(\frac{1}{16}\right)^{4}$$

Calculate \frac{1}{16} to the power of 4 and get \frac{1}{65536}.

$$\frac{1}{32}-\frac{1}{65536}$$

Least common multiple of 32 and 65536 is 65536. Convert \frac{1}{32} and \frac{1}{65536} to fractions with denominator 65536.

$$\frac{2048}{65536}-\frac{1}{65536}$$

Since \frac{2048}{65536} and \frac{1}{65536} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2048-1}{65536}$$

Subtract 1 from 2048 to get 2047.

$$\frac{2047}{65536}$$

Factor

$$\frac{23 \cdot 89}{2 ^ {16}} = 0.0312347412109375$$