Solve (4)^-1+(8)^-1div1/(frac{3{2})^-2}

$$( 4 ) ^ { - 1 } + ( 8 ) ^ { - 1 } \div \frac { 1 } { ( \frac { 3 } { 2 } ) ^ { - 2 } }$$

Evaluate

$$\frac{11}{36}\approx 0.305555556$$

Solution Steps

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

$$\frac{1}{4}+\frac{8^{-1}}{\frac{1}{\left(\frac{3}{2}\right)^{-2}}}$$

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

$$\frac{1}{4}+\frac{\frac{1}{8}}{\frac{1}{\left(\frac{3}{2}\right)^{-2}}}$$

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

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

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

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

Multiply 1 and \frac{9}{4} to get \frac{9}{4}.

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

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

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

Multiply \frac{1}{8} and \frac{4}{9} to get \frac{1}{18}.

$$\frac{1}{4}+\frac{1}{18}$$

Add \frac{1}{4} and \frac{1}{18} to get \frac{11}{36}.

$$\frac{11}{36}$$

Factor

$$\frac{11}{2 ^ {2} \cdot 3 ^ {2}} = 0.3055555555555556$$