Solve (1/3)^2-(1/16)^2

$$( \frac { 1 } { 3 } ) ^ { 2 } - ( \frac { 1 } { 16 } ) ^ { 2 }$$

Evaluate

$$\frac{247}{2304}\approx 0.107204861$$

Solution Steps

Calculate \frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{1}{9}-\left(\frac{1}{16}\right)^{2}$$

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

$$\frac{1}{9}-\frac{1}{256}$$

Least common multiple of 9 and 256 is 2304. Convert \frac{1}{9} and \frac{1}{256} to fractions with denominator 2304.

$$\frac{256}{2304}-\frac{9}{2304}$$

Since \frac{256}{2304} and \frac{9}{2304} have the same denominator, subtract them by subtracting their numerators.

$$\frac{256-9}{2304}$$

Subtract 9 from 256 to get 247.

$$\frac{247}{2304}$$

Factor

$$\frac{13 \cdot 19}{2 ^ {8} \cdot 3 ^ {2}} = 0.1072048611111111$$