Solve (9^-1*3^-3)^-1*(-1/3)^4

$$( 9 ^ { - 1 } \cdot 3 ^ { - 3 } ) ^ { - 1 } \cdot ( - \frac { 1 } { 3 } ) ^ { 4 }$$

Evaluate

$$3$$

Solution Steps

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

$$\left(\frac{1}{9}\times 3^{-3}\right)^{-1}\left(-\frac{1}{3}\right)^{4}$$

Calculate 3 to the power of -3 and get \frac{1}{27}.

$$\left(\frac{1}{9}\times \frac{1}{27}\right)^{-1}\left(-\frac{1}{3}\right)^{4}$$

Multiply \frac{1}{9} and \frac{1}{27} to get \frac{1}{243}.

$$\left(\frac{1}{243}\right)^{-1}\left(-\frac{1}{3}\right)^{4}$$

Calculate \frac{1}{243} to the power of -1 and get 243.

$$243\left(-\frac{1}{3}\right)^{4}$$

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

$$243\times \frac{1}{81}$$

Multiply 243 and \frac{1}{81} to get 3.

$$3$$

Factor

$$3$$