Solve |-5|-(sqrt{2}-1)^0+(-1/3)^-2+sqrt[3]{-27}

$$| - 5 | - ( \sqrt { 2 } - 1 ) ^ { 0 } + ( - \frac { 1 } { 3 } ) ^ { - 2 } + \sqrt[ 3 ] { - 27 }$$

Evaluate

$$10$$

Solution Steps

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -5 is 5.

$$5-\left(\sqrt{2}-1\right)^{0}+\left(-\frac{1}{3}\right)^{-2}+\sqrt[3]{-27}$$

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

$$5-1+\left(-\frac{1}{3}\right)^{-2}+\sqrt[3]{-27}$$

Subtract 1 from 5 to get 4.

$$4+\left(-\frac{1}{3}\right)^{-2}+\sqrt[3]{-27}$$

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

$$4+9+\sqrt[3]{-27}$$

Add 4 and 9 to get 13.

$$13+\sqrt[3]{-27}$$

Calculate \sqrt[3]{-27} and get -3.

$$13-3$$

Subtract 3 from 13 to get 10.

$$10$$

Factor

$$2\times 5$$