Solve 1/(frac{1{2})^-2}+27/(frac{2{3})^-3}

$$\frac { 1 } { ( \frac { 1 } { 2 } ) ^ { - 2 } } + \frac { 27 } { ( \frac { 2 } { 3 } ) ^ { - 3 } }$$

Evaluate

$$\frac{33}{4}=8.25$$

Solution Steps

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

$$\frac{1}{4}+\frac{27}{\left(\frac{2}{3}\right)^{-3}}$$

Calculate \frac{2}{3} to the power of -3 and get \frac{27}{8}.

$$\frac{1}{4}+\frac{27}{\frac{27}{8}}$$

Divide 27 by \frac{27}{8} by multiplying 27 by the reciprocal of \frac{27}{8}.

$$\frac{1}{4}+27\times \frac{8}{27}$$

Multiply 27 and \frac{8}{27} to get 8.

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

Add \frac{1}{4} and 8 to get \frac{33}{4}.

$$\frac{33}{4}$$

Factor

$$\frac{3 \cdot 11}{2 ^ {2}} = 8\frac{1}{4} = 8.25$$