Solve (2/5)^4div(4/25)^-2

$$( \frac { 2 } { 5 } ) ^ { 4 } \div ( \frac { 4 } { 25 } ) ^ { - 2 }$$

Evaluate

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

Solution Steps

Calculate \frac{2}{5} to the power of 4 and get \frac{16}{625}.

$$\frac{\frac{16}{625}}{\left(\frac{4}{25}\right)^{-2}}$$

Calculate \frac{4}{25} to the power of -2 and get \frac{625}{16}.

$$\frac{\frac{16}{625}}{\frac{625}{16}}$$

Divide \frac{16}{625} by \frac{625}{16} by multiplying \frac{16}{625} by the reciprocal of \frac{625}{16}.

$$\frac{16}{625}\times \frac{16}{625}$$

Multiply \frac{16}{625} and \frac{16}{625} to get \frac{256}{390625}.

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

Factor

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