Solve [(-6/5)^-2*(-6/5)^-3]^-1div(36/125)^-1

$$[ ( \frac { - 6 } { 5 } ) ^ { - 2 } \times ( - \frac { 6 } { 5 } ) ^ { - 3 } ] ^ { - 1 } \div ( \frac { 36 } { 125 } ) ^ { - 1 }$$

Evaluate

$$-\frac{279936}{390625}=-0.71663616$$

Solution Steps

Fraction \frac{-6}{5} can be rewritten as -\frac{6}{5} by extracting the negative sign.

$$\frac{\left(\left(-\frac{6}{5}\right)^{-2}\left(-\frac{6}{5}\right)^{-3}\right)^{-1}}{\left(\frac{36}{125}\right)^{-1}}$$

Calculate -\frac{6}{5} to the power of -2 and get \frac{25}{36}.

$$\frac{\left(\frac{25}{36}\left(-\frac{6}{5}\right)^{-3}\right)^{-1}}{\left(\frac{36}{125}\right)^{-1}}$$

Calculate -\frac{6}{5} to the power of -3 and get -\frac{125}{216}.

$$\frac{\left(\frac{25}{36}\left(-\frac{125}{216}\right)\right)^{-1}}{\left(\frac{36}{125}\right)^{-1}}$$

Multiply \frac{25}{36} and -\frac{125}{216} to get -\frac{3125}{7776}.

$$\frac{\left(-\frac{3125}{7776}\right)^{-1}}{\left(\frac{36}{125}\right)^{-1}}$$

Calculate -\frac{3125}{7776} to the power of -1 and get -\frac{7776}{3125}.

$$\frac{-\frac{7776}{3125}}{\left(\frac{36}{125}\right)^{-1}}$$

Calculate \frac{36}{125} to the power of -1 and get \frac{125}{36}.

$$\frac{-\frac{7776}{3125}}{\frac{125}{36}}$$

Divide -\frac{7776}{3125} by \frac{125}{36} by multiplying -\frac{7776}{3125} by the reciprocal of \frac{125}{36}.

$$-\frac{7776}{3125}\times \frac{36}{125}$$

Multiply -\frac{7776}{3125} and \frac{36}{125} to get -\frac{279936}{390625}.

$$-\frac{279936}{390625}$$

Factor

$$-\frac{279936}{390625} = -0.71663616$$