Solve (-3/4)^3+(-5/8)^3+(11/8)^3

$$( \frac { - 3 } { 4 } ) ^ { 3 } + ( \frac { - 5 } { 8 } ) ^ { 3 } + ( \frac { 11 } { 8 } ) ^ { 3 }$$

Evaluate

$$\frac{495}{256}=1.93359375$$

Solution Steps

Fraction \frac{-3}{4} can be rewritten as -\frac{3}{4} by extracting the negative sign.

$$\left(-\frac{3}{4}\right)^{3}+\left(\frac{-5}{8}\right)^{3}+\left(\frac{11}{8}\right)^{3}$$

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

$$-\frac{27}{64}+\left(\frac{-5}{8}\right)^{3}+\left(\frac{11}{8}\right)^{3}$$

Fraction \frac{-5}{8} can be rewritten as -\frac{5}{8} by extracting the negative sign.

$$-\frac{27}{64}+\left(-\frac{5}{8}\right)^{3}+\left(\frac{11}{8}\right)^{3}$$

Calculate -\frac{5}{8} to the power of 3 and get -\frac{125}{512}.

$$-\frac{27}{64}-\frac{125}{512}+\left(\frac{11}{8}\right)^{3}$$

Subtract \frac{125}{512} from -\frac{27}{64} to get -\frac{341}{512}.

$$-\frac{341}{512}+\left(\frac{11}{8}\right)^{3}$$

Calculate \frac{11}{8} to the power of 3 and get \frac{1331}{512}.

$$-\frac{341}{512}+\frac{1331}{512}$$

Add -\frac{341}{512} and \frac{1331}{512} to get \frac{495}{256}.

$$\frac{495}{256}$$

Factor

$$\frac{3 ^ {2} \cdot 5 \cdot 11}{2 ^ {8}} = 1\frac{239}{256} = 1.93359375$$