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

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

Evaluate

$$\frac{256}{390625}=0.00065536$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{\left(\frac{2}{5}\right)^{6}}{\left(\frac{5}{2}\right)^{2}}$$

Calculate \frac{2}{5} to the power of 6 and get \frac{64}{15625}.

$$\frac{\frac{64}{15625}}{\left(\frac{5}{2}\right)^{2}}$$

Calculate \frac{5}{2} to the power of 2 and get \frac{25}{4}.

$$\frac{\frac{64}{15625}}{\frac{25}{4}}$$

Divide \frac{64}{15625} by \frac{25}{4} by multiplying \frac{64}{15625} by the reciprocal of \frac{25}{4}.

$$\frac{64}{15625}\times \frac{4}{25}$$

Multiply \frac{64}{15625} and \frac{4}{25} to get \frac{256}{390625}.

$$\frac{256}{390625}$$

Factor

$$\frac{2 ^ {8}}{5 ^ {8}} = 0.00065536$$