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

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

Evaluate

$$-\frac{113}{64}=-1.765625$$

Solution Steps

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

$$3\times \frac{1}{64}-\left(\frac{1}{4}\right)^{2}+\frac{1}{4}-2$$

Multiply 3 and \frac{1}{64} to get \frac{3}{64}.

$$\frac{3}{64}-\left(\frac{1}{4}\right)^{2}+\frac{1}{4}-2$$

Calculate \frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$\frac{3}{64}-\frac{1}{16}+\frac{1}{4}-2$$

Least common multiple of 64 and 16 is 64. Convert \frac{3}{64} and \frac{1}{16} to fractions with denominator 64.

$$\frac{3}{64}-\frac{4}{64}+\frac{1}{4}-2$$

Since \frac{3}{64} and \frac{4}{64} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-4}{64}+\frac{1}{4}-2$$

Subtract 4 from 3 to get -1.

$$-\frac{1}{64}+\frac{1}{4}-2$$

Least common multiple of 64 and 4 is 64. Convert -\frac{1}{64} and \frac{1}{4} to fractions with denominator 64.

$$-\frac{1}{64}+\frac{16}{64}-2$$

Since -\frac{1}{64} and \frac{16}{64} have the same denominator, add them by adding their numerators.

$$\frac{-1+16}{64}-2$$

Add -1 and 16 to get 15.

$$\frac{15}{64}-2$$

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

$$\frac{15}{64}-\frac{128}{64}$$

Since \frac{15}{64} and \frac{128}{64} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15-128}{64}$$

Subtract 128 from 15 to get -113.

$$-\frac{113}{64}$$

Factor

$$-\frac{113}{64} = -1\frac{49}{64} = -1.765625$$