Solve (-1)^2015-(1/3)^-2+(2-sqrt{2})^0-|-2|

$$( - 1 ) ^ { 2015 } - ( \frac { 1 } { 3 } ) ^ { - 2 } + ( 2 - \sqrt { 2 } ) ^ { 0 } - | - 2 |$$

Evaluate

$$-11$$

Solution Steps

Calculate -1 to the power of 2015 and get -1.

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

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

$$-1-9+\left(2-\sqrt{2}\right)^{0}-|-2|$$

Subtract 9 from -1 to get -10.

$$-10+\left(2-\sqrt{2}\right)^{0}-|-2|$$

Calculate 2-\sqrt{2} to the power of 0 and get 1.

$$-10+1-|-2|$$

Add -10 and 1 to get -9.

$$-9-|-2|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -2 is 2.

$$-9-2$$

Subtract 2 from -9 to get -11.

$$-11$$

Factor

$$-11$$