Solve (2/3)^2:(2/5)^3=

$$( \frac { 2 } { 3 } ) ^ { 2 } : ( \frac { 2 } { 5 } ) ^ { 3 } =$$

Evaluate

$$\frac{125}{18}\approx 6.944444444$$

Solution Steps

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

$$\frac{\frac{4}{9}}{\left(\frac{2}{5}\right)^{3}}$$

Calculate \frac{2}{5} to the power of 3 and get \frac{8}{125}.

$$\frac{\frac{4}{9}}{\frac{8}{125}}$$

Divide \frac{4}{9} by \frac{8}{125} by multiplying \frac{4}{9} by the reciprocal of \frac{8}{125}.

$$\frac{4}{9}\times \frac{125}{8}$$

Multiply \frac{4}{9} times \frac{125}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 125}{9\times 8}$$

Do the multiplications in the fraction \frac{4\times 125}{9\times 8}.

$$\frac{500}{72}$$

Reduce the fraction \frac{500}{72} to lowest terms by extracting and canceling out 4.

$$\frac{125}{18}$$

Factor

$$\frac{5 ^ {3}}{2 \cdot 3 ^ {2}} = 6\frac{17}{18} = 6.944444444444445$$