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

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

Evaluate

$$-11$$

Solution Steps

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

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

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

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

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

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

Divide 1 by \frac{1}{9} by multiplying 1 by the reciprocal of \frac{1}{9}.

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

Multiply 1 and 9 to 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

$$-11$$