Solve (-4/5)^7div(-4/5)^9

$$( - \frac { 4 } { 5 } ) ^ { 7 } \div ( - \frac { 4 } { 5 } ) ^ { 9 }$$

Evaluate

$$\frac{25}{16}=1.5625$$

Solution Steps

Rewrite \left(-\frac{4}{5}\right)^{9} as \left(-\frac{4}{5}\right)^{7}\left(-\frac{4}{5}\right)^{2}. Cancel out \left(-\frac{4}{5}\right)^{7} in both numerator and denominator.

$$\frac{1}{\left(-\frac{4}{5}\right)^{2}}$$

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

$$\frac{1}{\frac{16}{25}}$$

Divide 1 by \frac{16}{25} by multiplying 1 by the reciprocal of \frac{16}{25}.

$$1\times \frac{25}{16}$$

Multiply 1 and \frac{25}{16} to get \frac{25}{16}.

$$\frac{25}{16}$$

Factor

$$\frac{5 ^ {2}}{2 ^ {4}} = 1\frac{9}{16} = 1.5625$$