Solve (-3^-4/3^-6)^-1

$$( \frac { - 3 ^ { - 4 } } { 3 ^ { - 6 } } ) ^ { - 1 }$$

Evaluate

$$-\frac{1}{9}\approx -0.111111111$$

Solution Steps

Calculate 3 to the power of -4 and get \frac{1}{81}.

$$\left(\frac{-\frac{1}{81}}{3^{-6}}\right)^{-1}$$

Calculate 3 to the power of -6 and get \frac{1}{729}.

$$\left(\frac{-\frac{1}{81}}{\frac{1}{729}}\right)^{-1}$$

Divide -\frac{1}{81} by \frac{1}{729} by multiplying -\frac{1}{81} by the reciprocal of \frac{1}{729}.

$$\left(-\frac{1}{81}\times 729\right)^{-1}$$

Multiply -\frac{1}{81} and 729 to get -9.

$$\left(-9\right)^{-1}$$

Calculate -9 to the power of -1 and get -\frac{1}{9}.

$$-\frac{1}{9}$$

Factor

$$-\frac{1}{9} = -0.1111111111111111$$