Solve -9^-2+(9^1/6^2)^-1

$$- 9 ^ { - 2 } + ( \frac { 9 ^ { 1 } } { 6 ^ { 2 } } ) ^ { - 1 }$$

Evaluate

$$\frac{323}{81}\approx 3.987654321$$

Solution Steps

Calculate 9 to the power of -2 and get \frac{1}{81}.

$$-\frac{1}{81}+\left(\frac{9^{1}}{6^{2}}\right)^{-1}$$

Calculate 9 to the power of 1 and get 9.

$$-\frac{1}{81}+\left(\frac{9}{6^{2}}\right)^{-1}$$

Calculate 6 to the power of 2 and get 36.

$$-\frac{1}{81}+\left(\frac{9}{36}\right)^{-1}$$

Reduce the fraction \frac{9}{36} to lowest terms by extracting and canceling out 9.

$$-\frac{1}{81}+\left(\frac{1}{4}\right)^{-1}$$

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

$$-\frac{1}{81}+4$$

Add -\frac{1}{81} and 4 to get \frac{323}{81}.

$$\frac{323}{81}$$

Factor

$$\frac{17 \cdot 19}{3 ^ {4}} = 3\frac{80}{81} = 3.9876543209876543$$