Solve -3divsqrt{3}*(sqrt{3})^-1+(-1)^201+4-3

$$- 3 \div \sqrt { 3 } \times ( \sqrt { 3 } ) ^ { - 1 } + ( - 1 ) ^ { 201 } + 4 - 3$$

Evaluate

$$-1$$

Solution Steps

Rationalize the denominator of \frac{-3}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{-3\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\left(\sqrt{3}\right)^{-1}+\left(-1\right)^{201}+4-3$$

The square of \sqrt{3} is 3.

$$\frac{-3\sqrt{3}}{3}\left(\sqrt{3}\right)^{-1}+\left(-1\right)^{201}+4-3$$

Cancel out 3 and 3.

$$-\sqrt{3}\left(\sqrt{3}\right)^{-1}+\left(-1\right)^{201}+4-3$$

Multiply \sqrt{3} and \left(\sqrt{3}\right)^{-1} to get 1.

$$-1+\left(-1\right)^{201}+4-3$$

Calculate -1 to the power of 201 and get -1.

$$-1-1+4-3$$

Subtract 1 from -1 to get -2.

$$-2+4-3$$

Add -2 and 4 to get 2.

$$2-3$$

Subtract 3 from 2 to get -1.

$$-1$$

Factor

$$-1$$