Solve (5/8)^2*(2/5-9/25)-1/8*frac{1}{16}

$$( \frac { 5 } { 8 } ) ^ { 2 } \cdot ( \frac { 2 } { 5 } - \frac { 9 } { 25 } ) - \frac { 1 } { 8 } \cdot \frac { 1 } { 16 }$$

Evaluate

$$\frac{1}{128}=0.0078125$$

Solution Steps

Calculate \frac{5}{8} to the power of 2 and get \frac{25}{64}.

$$\frac{25}{64}\left(\frac{2}{5}-\frac{9}{25}\right)-\frac{1}{8}\times \frac{1}{16}$$

Least common multiple of 5 and 25 is 25. Convert \frac{2}{5} and \frac{9}{25} to fractions with denominator 25.

$$\frac{25}{64}\left(\frac{10}{25}-\frac{9}{25}\right)-\frac{1}{8}\times \frac{1}{16}$$

Since \frac{10}{25} and \frac{9}{25} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25}{64}\times \frac{10-9}{25}-\frac{1}{8}\times \frac{1}{16}$$

Subtract 9 from 10 to get 1.

$$\frac{25}{64}\times \frac{1}{25}-\frac{1}{8}\times \frac{1}{16}$$

Multiply \frac{25}{64} times \frac{1}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{25\times 1}{64\times 25}-\frac{1}{8}\times \frac{1}{16}$$

Cancel out 25 in both numerator and denominator.

$$\frac{1}{64}-\frac{1}{8}\times \frac{1}{16}$$

Multiply \frac{1}{8} times \frac{1}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{64}-\frac{1\times 1}{8\times 16}$$

Do the multiplications in the fraction \frac{1\times 1}{8\times 16}.

$$\frac{1}{64}-\frac{1}{128}$$

Least common multiple of 64 and 128 is 128. Convert \frac{1}{64} and \frac{1}{128} to fractions with denominator 128.

$$\frac{2}{128}-\frac{1}{128}$$

Since \frac{2}{128} and \frac{1}{128} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-1}{128}$$

Subtract 1 from 2 to get 1.

$$\frac{1}{128}$$

Factor

$$\frac{1}{2 ^ {7}} = 0.0078125$$