Solve frac{(-2)^{0}+(-1)^{2}+(1/3)^2}{(-2)^2+(-3)^2-(-1)^0}

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

Evaluate

$$\frac{19}{108}\approx 0.175925926$$

Solution Steps

Calculate -2 to the power of 0 and get 1.

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

Calculate -1 to the power of 2 and get 1.

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

Add 1 and 1 to get 2.

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

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

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

Add 2 and \frac{1}{9} to get \frac{19}{9}.

$$\frac{\frac{19}{9}}{\left(-2\right)^{2}+\left(-3\right)^{2}-\left(-1\right)^{0}}$$

Calculate -2 to the power of 2 and get 4.

$$\frac{\frac{19}{9}}{4+\left(-3\right)^{2}-\left(-1\right)^{0}}$$

Calculate -3 to the power of 2 and get 9.

$$\frac{\frac{19}{9}}{4+9-\left(-1\right)^{0}}$$

Add 4 and 9 to get 13.

$$\frac{\frac{19}{9}}{13-\left(-1\right)^{0}}$$

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

$$\frac{\frac{19}{9}}{13-1}$$

Subtract 1 from 13 to get 12.

$$\frac{\frac{19}{9}}{12}$$

Express \frac{\frac{19}{9}}{12} as a single fraction.

$$\frac{19}{9\times 12}$$

Multiply 9 and 12 to get 108.

$$\frac{19}{108}$$

Factor

$$\frac{19}{2 ^ {2} \cdot 3 ^ {3}} = 0.17592592592592593$$