Solve (64/27)^-frac{2{3}}div(9/16)^frac{3{2}}

$$( \frac { 64 } { 27 } ) ^ { - \frac { 2 } { 3 } } \div ( \frac { 9 } { 16 } ) ^ { \frac { 3 } { 2 } }$$

Evaluate

$$\frac{4}{3}\approx 1.333333333$$

Solution Steps

Calculate \frac{64}{27} to the power of -\frac{2}{3} and get \frac{9}{16}.

$$\frac{\frac{9}{16}}{\left(\frac{9}{16}\right)^{\frac{3}{2}}}$$

Calculate \frac{9}{16} to the power of \frac{3}{2} and get \frac{27}{64}.

$$\frac{\frac{9}{16}}{\frac{27}{64}}$$

Divide \frac{9}{16} by \frac{27}{64} by multiplying \frac{9}{16} by the reciprocal of \frac{27}{64}.

$$\frac{9}{16}\times \frac{64}{27}$$

Multiply \frac{9}{16} and \frac{64}{27} to get \frac{4}{3}.

$$\frac{4}{3}$$

Factor

$$\frac{2 ^ {2}}{3} = 1\frac{1}{3} = 1.3333333333333333$$