Solve [{(-1/3)^2}^-2]^-1

$$[ \{ ( \frac { - 1 } { 3 } ) ^ { 2 } \} ^ { - 2 } ] ^ { - 1 }$$

Evaluate

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

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and -2 to get -4.

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

Fraction \frac{-1}{3} can be rewritten as -\frac{1}{3} by extracting the negative sign.

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

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

$$81^{-1}$$

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

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

Factor

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