Solve (2/3)^-5div(-2/3)^-7

$$( \frac { 2 } { 3 } ) ^ { - 5 } \div ( - \frac { 2 } { 3 } ) ^ { - 7 }$$

Evaluate

$$-\frac{4}{9}\approx -0.444444444$$

Solution Steps

Calculate \frac{2}{3} to the power of -5 and get \frac{243}{32}.

$$\frac{\frac{243}{32}}{\left(-\frac{2}{3}\right)^{-7}}$$

Calculate -\frac{2}{3} to the power of -7 and get -\frac{2187}{128}.

$$\frac{\frac{243}{32}}{-\frac{2187}{128}}$$

Divide \frac{243}{32} by -\frac{2187}{128} by multiplying \frac{243}{32} by the reciprocal of -\frac{2187}{128}.

$$\frac{243}{32}\left(-\frac{128}{2187}\right)$$

Multiply \frac{243}{32} and -\frac{128}{2187} to get -\frac{4}{9}.

$$-\frac{4}{9}$$

Factor

$$-\frac{4}{9} = -0.4444444444444444$$