Solve (2/5)^2*(2/5)^3div3/9*9/25

$$( 2 / 5 ) ^ { 2 } \times ( 2 / 5 ) ^ { 3 } \div \frac { 3 } { 9 } \times \frac { 9 } { 25 }$$

Evaluate

$$\frac{864}{78125}=0.0110592$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{\left(\frac{2}{5}\right)^{5}}{\frac{3}{9}}\times \frac{9}{25}$$

Calculate \frac{2}{5} to the power of 5 and get \frac{32}{3125}.

$$\frac{\frac{32}{3125}}{\frac{3}{9}}\times \frac{9}{25}$$

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{32}{3125}}{\frac{1}{3}}\times \frac{9}{25}$$

Divide \frac{32}{3125} by \frac{1}{3} by multiplying \frac{32}{3125} by the reciprocal of \frac{1}{3}.

$$\frac{32}{3125}\times 3\times \frac{9}{25}$$

Express \frac{32}{3125}\times 3 as a single fraction.

$$\frac{32\times 3}{3125}\times \frac{9}{25}$$

Multiply 32 and 3 to get 96.

$$\frac{96}{3125}\times \frac{9}{25}$$

Multiply \frac{96}{3125} times \frac{9}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{96\times 9}{3125\times 25}$$

Do the multiplications in the fraction \frac{96\times 9}{3125\times 25}.

$$\frac{864}{78125}$$

Factor

$$\frac{2 ^ {5} \cdot 3 ^ {3}}{5 ^ {7}} = 0.0110592$$