Solve (1+1/2)^2/(frac{1{2})^3}

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

Evaluate

$$18$$

Solution Steps

Add 1 and \frac{1}{2} to get \frac{3}{2}.

$$\frac{\left(\frac{3}{2}\right)^{2}}{\left(\frac{1}{2}\right)^{3}}$$

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

$$\frac{\frac{9}{4}}{\left(\frac{1}{2}\right)^{3}}$$

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

$$\frac{\frac{9}{4}}{\frac{1}{8}}$$

Divide \frac{9}{4} by \frac{1}{8} by multiplying \frac{9}{4} by the reciprocal of \frac{1}{8}.

$$\frac{9}{4}\times 8$$

Multiply \frac{9}{4} and 8 to get 18.

$$18$$

Factor

$$2\times 3^{2}$$