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

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

Evaluate

$$\frac{59}{64}=0.921875$$

Solution Steps

Calculate \frac{3}{4} to the power of 3 and get \frac{27}{64}.

$$\frac{27}{64}-2\times \frac{3}{4}+2$$

Express 2\times \frac{3}{4} as a single fraction.

$$\frac{27}{64}-\frac{2\times 3}{4}+2$$

Multiply 2 and 3 to get 6.

$$\frac{27}{64}-\frac{6}{4}+2$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{27}{64}-\frac{3}{2}+2$$

Least common multiple of 64 and 2 is 64. Convert \frac{27}{64} and \frac{3}{2} to fractions with denominator 64.

$$\frac{27}{64}-\frac{96}{64}+2$$

Since \frac{27}{64} and \frac{96}{64} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27-96}{64}+2$$

Subtract 96 from 27 to get -69.

$$-\frac{69}{64}+2$$

Convert 2 to fraction \frac{128}{64}.

$$-\frac{69}{64}+\frac{128}{64}$$

Since -\frac{69}{64} and \frac{128}{64} have the same denominator, add them by adding their numerators.

$$\frac{-69+128}{64}$$

Add -69 and 128 to get 59.

$$\frac{59}{64}$$

Factor

$$\frac{59}{2 ^ {6}} = 0.921875$$