Solve -3^-2+(x-1)^0-3^-3*(-2/3)^-2

$$- 3 ^ { - 2 } + ( x - 1 ) ^ { 0 } - 3 ^ { - 3 } \times ( - \frac { 2 } { 3 } ) ^ { - 2 }$$

Evaluate

$$\frac{29}{36}\approx 0.805555556$$

Solution Steps

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$-\frac{1}{9}+\left(x-1\right)^{0}-3^{-3}\left(-\frac{2}{3}\right)^{-2}$$

Calculate x-1 to the power of 0 and get 1.

$$-\frac{1}{9}+1-3^{-3}\left(-\frac{2}{3}\right)^{-2}$$

Add -\frac{1}{9} and 1 to get \frac{8}{9}.

$$\frac{8}{9}-3^{-3}\left(-\frac{2}{3}\right)^{-2}$$

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

$$\frac{8}{9}-\frac{1}{27}\left(-\frac{2}{3}\right)^{-2}$$

Calculate -\frac{2}{3} to the power of -2 and get \frac{9}{4}.

$$\frac{8}{9}-\frac{1}{27}\times \frac{9}{4}$$

Multiply \frac{1}{27} and \frac{9}{4} to get \frac{1}{12}.

$$\frac{8}{9}-\frac{1}{12}$$

Subtract \frac{1}{12} from \frac{8}{9} to get \frac{29}{36}.

$$\frac{29}{36}$$

Factor

$$\frac{29}{2 ^ {2} \cdot 3 ^ {2}} = 0.8055555555555556$$

Solution Steps

Factor out common term 36-4-3 by using distributive property.

$$\left(36-4-3\right)\left(-\frac{1}{261}+\frac{1}{29}-\frac{1}{348}\right)$$

Consider -\frac{1}{261}+\frac{1}{29}-\frac{1}{348}. Simplify.

$$\frac{1}{36}$$

Rewrite the complete factored expression. Simplify.

$$\frac{29}{36}$$