Solve (3/4)^2-1/4-(-3/8)^2+(1/4)^3

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

Evaluate

$$\frac{3}{16}=0.1875$$

Solution Steps

Calculate \frac{3}{4} to the power of 2 and get \frac{9}{16}.

$$\frac{9}{16}-\frac{1}{4}-\left(-\frac{3}{8}\right)^{2}+\left(\frac{1}{4}\right)^{3}$$

Least common multiple of 16 and 4 is 16. Convert \frac{9}{16} and \frac{1}{4} to fractions with denominator 16.

$$\frac{9}{16}-\frac{4}{16}-\left(-\frac{3}{8}\right)^{2}+\left(\frac{1}{4}\right)^{3}$$

Since \frac{9}{16} and \frac{4}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-4}{16}-\left(-\frac{3}{8}\right)^{2}+\left(\frac{1}{4}\right)^{3}$$

Subtract 4 from 9 to get 5.

$$\frac{5}{16}-\left(-\frac{3}{8}\right)^{2}+\left(\frac{1}{4}\right)^{3}$$

Calculate -\frac{3}{8} to the power of 2 and get \frac{9}{64}.

$$\frac{5}{16}-\frac{9}{64}+\left(\frac{1}{4}\right)^{3}$$

Least common multiple of 16 and 64 is 64. Convert \frac{5}{16} and \frac{9}{64} to fractions with denominator 64.

$$\frac{20}{64}-\frac{9}{64}+\left(\frac{1}{4}\right)^{3}$$

Since \frac{20}{64} and \frac{9}{64} have the same denominator, subtract them by subtracting their numerators.

$$\frac{20-9}{64}+\left(\frac{1}{4}\right)^{3}$$

Subtract 9 from 20 to get 11.

$$\frac{11}{64}+\left(\frac{1}{4}\right)^{3}$$

Calculate \frac{1}{4} to the power of 3 and get \frac{1}{64}.

$$\frac{11}{64}+\frac{1}{64}$$

Since \frac{11}{64} and \frac{1}{64} have the same denominator, add them by adding their numerators.

$$\frac{11+1}{64}$$

Add 11 and 1 to get 12.

$$\frac{12}{64}$$

Reduce the fraction \frac{12}{64} to lowest terms by extracting and canceling out 4.

$$\frac{3}{16}$$

Factor

$$\frac{3}{2 ^ {4}} = 0.1875$$