Solve (-4/5)^2div(2/5)^3

$$( - \frac { 4 } { 5 } ) ^ { 2 } \div ( \frac { 2 } { 5 } ) ^ { 3 }$$

Evaluate

$$10$$

Solution Steps

Calculate -\frac{4}{5} to the power of 2 and get \frac{16}{25}.

$$\frac{\frac{16}{25}}{\left(\frac{2}{5}\right)^{3}}$$

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

$$\frac{\frac{16}{25}}{\frac{8}{125}}$$

Divide \frac{16}{25} by \frac{8}{125} by multiplying \frac{16}{25} by the reciprocal of \frac{8}{125}.

$$\frac{16}{25}\times \frac{125}{8}$$

Multiply \frac{16}{25} times \frac{125}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{16\times 125}{25\times 8}$$

Do the multiplications in the fraction \frac{16\times 125}{25\times 8}.

$$\frac{2000}{200}$$

Divide 2000 by 200 to get 10.

$$10$$

Factor

$$2\times 5$$