Solve (2/3)^-2*(2/5)^-1div12/3

$$( \frac { 2 } { 3 } ) ^ { - 2 } \times ( \frac { 2 } { 5 } ) ^ { - 1 } \div 1 \frac { 2 } { 3 }$$

Evaluate

$$\frac{27}{8}=3.375$$

Solution Steps

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

$$\frac{\frac{9}{4}\times \left(\frac{2}{5}\right)^{-1}}{\frac{1\times 3+2}{3}}$$

Calculate \frac{2}{5} to the power of -1 and get \frac{5}{2}.

$$\frac{\frac{9}{4}\times \frac{5}{2}}{\frac{1\times 3+2}{3}}$$

Multiply \frac{9}{4} and \frac{5}{2} to get \frac{45}{8}.

$$\frac{\frac{45}{8}}{\frac{1\times 3+2}{3}}$$

Multiply 1 and 3 to get 3.

$$\frac{\frac{45}{8}}{\frac{3+2}{3}}$$

Add 3 and 2 to get 5.

$$\frac{\frac{45}{8}}{\frac{5}{3}}$$

Divide \frac{45}{8} by \frac{5}{3} by multiplying \frac{45}{8} by the reciprocal of \frac{5}{3}.

$$\frac{45}{8}\times \frac{3}{5}$$

Multiply \frac{45}{8} and \frac{3}{5} to get \frac{27}{8}.

$$\frac{27}{8}$$

Factor

$$\frac{3 ^ {3}}{2 ^ {3}} = 3\frac{3}{8} = 3.375$$