Solve -2^3+{left(1/3right)}^-2-sqrt{8}sin(45)

$${ -2 }^{ 3 } + { \left( \frac{ 1 }{ 3 } \right) }^{ -2 } - \sqrt{ 8 } \sin ( 45 )$$

Evaluate

$$-1$$

Solution Steps

Calculate -2 to the power of 3 and get -8.

$$-8+\left(\frac{1}{3}\right)^{-2}-\sqrt{8}\sin(45)$$

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

$$-8+9-\sqrt{8}\sin(45)$$

Add -8 and 9 to get 1.

$$1-\sqrt{8}\sin(45)$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$1-2\sqrt{2}\sin(45)$$

Get the value of \sin(45) from trigonometric values table.

$$1-2\sqrt{2}\times \frac{\sqrt{2}}{2}$$

Cancel out 2 and 2.

$$1-\sqrt{2}\sqrt{2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$1-2$$

Subtract 2 from 1 to get -1.

$$-1$$