Solve (3/2)^2-(1/2)^3+(1/7)^2*(2/7)^-2

$$( \frac { 3 } { 2 } ) ^ { 2 } - ( \frac { 1 } { 2 } ) ^ { 3 } + ( \frac { 1 } { 7 } ) ^ { 2 } \cdot ( \frac { 2 } { 7 } ) ^ { - 2 }$$

Evaluate

$$\frac{19}{8}=2.375$$

Solution Steps

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

$$\frac{9}{4}-\left(\frac{1}{2}\right)^{3}+\left(\frac{1}{7}\right)^{2}\times \left(\frac{2}{7}\right)^{-2}$$

Calculate \frac{1}{2} to the power of 3 and get \frac{1}{8}.

$$\frac{9}{4}-\frac{1}{8}+\left(\frac{1}{7}\right)^{2}\times \left(\frac{2}{7}\right)^{-2}$$

Subtract \frac{1}{8} from \frac{9}{4} to get \frac{17}{8}.

$$\frac{17}{8}+\left(\frac{1}{7}\right)^{2}\times \left(\frac{2}{7}\right)^{-2}$$

Calculate \frac{1}{7} to the power of 2 and get \frac{1}{49}.

$$\frac{17}{8}+\frac{1}{49}\times \left(\frac{2}{7}\right)^{-2}$$

Calculate \frac{2}{7} to the power of -2 and get \frac{49}{4}.

$$\frac{17}{8}+\frac{1}{49}\times \frac{49}{4}$$

Multiply \frac{1}{49} and \frac{49}{4} to get \frac{1}{4}.

$$\frac{17}{8}+\frac{1}{4}$$

Add \frac{17}{8} and \frac{1}{4} to get \frac{19}{8}.

$$\frac{19}{8}$$

Factor

$$\frac{19}{2 ^ {3}} = 2\frac{3}{8} = 2.375$$