Solve {left(frac{-2/5right)}^6{left(-2/5right)}^4}{{left(4/25right)}^2}

$$\frac{ { \left( \frac{ -2 }{ 5 } \right) }^{ 6 } { \left( \frac{ -2 }{ 5 } \right) }^{ 4 } }{ { \left( \frac{ 4 }{ 25 } \right) }^{ 2 } }$$

Evaluate

$$\frac{64}{15625}=0.004096$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 4 to get 10.

$$\frac{\left(\frac{-2}{5}\right)^{10}}{\left(\frac{4}{25}\right)^{2}}$$

Fraction \frac{-2}{5} can be rewritten as -\frac{2}{5} by extracting the negative sign.

$$\frac{\left(-\frac{2}{5}\right)^{10}}{\left(\frac{4}{25}\right)^{2}}$$

Calculate -\frac{2}{5} to the power of 10 and get \frac{1024}{9765625}.

$$\frac{\frac{1024}{9765625}}{\left(\frac{4}{25}\right)^{2}}$$

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

$$\frac{\frac{1024}{9765625}}{\frac{16}{625}}$$

Divide \frac{1024}{9765625} by \frac{16}{625} by multiplying \frac{1024}{9765625} by the reciprocal of \frac{16}{625}.

$$\frac{1024}{9765625}\times \frac{625}{16}$$

Multiply \frac{1024}{9765625} and \frac{625}{16} to get \frac{64}{15625}.

$$\frac{64}{15625}$$

Factor

$$\frac{2 ^ {6}}{5 ^ {6}} = 0.004096$$