Solve (3^2)^-1/3^-2*3^4

$$\frac { ( 3 ^ { 2 } ) ^ { - 1 } } { 3 ^ { - 2 } \cdot 3 ^ { 4 } }$$

Evaluate

$$\frac{1}{81}\approx 0.012345679$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and -1 to get -2.

$$\frac{3^{-2}}{3^{-2}\times 3^{4}}$$

To multiply powers of the same base, add their exponents. Add -2 and 4 to get 2.

$$\frac{3^{-2}}{3^{2}}$$

Rewrite 3^{2} as 3^{-2}\times 3^{4}. Cancel out 3^{-2} in both numerator and denominator.

$$\frac{1}{3^{4}}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{1}{81}$$

Factor

$$\frac{1}{3 ^ {4}} = 0.012345679012345678$$