Solve 1+1/3:(1/3)^-2-sqrt{12}cos30^circ+|-4|-(-2)^0

$$1 + \frac { 1 } { 3 } : ( \frac { 1 } { 3 } ) ^ { - 2 } - \sqrt { 12 } \cos 30 ^ { \circ } + | - 4 | - ( - 2 ) ^ { 0 }$$

Evaluate

$$\frac{28}{27}\approx 1.037037037$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -2 from 1 to get 3.

$$1+\left(\frac{1}{3}\right)^{3}-\sqrt{12}\cos(30)+|-4|-\left(-2\right)^{0}$$

Calculate \frac{1}{3} to the power of 3 and get \frac{1}{27}.

$$1+\frac{1}{27}-\sqrt{12}\cos(30)+|-4|-\left(-2\right)^{0}$$

Add 1 and \frac{1}{27} to get \frac{28}{27}.

$$\frac{28}{27}-\sqrt{12}\cos(30)+|-4|-\left(-2\right)^{0}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\frac{28}{27}-2\sqrt{3}\cos(30)+|-4|-\left(-2\right)^{0}$$

Get the value of \cos(30) from trigonometric values table.

$$\frac{28}{27}-2\sqrt{3}\times \frac{\sqrt{3}}{2}+|-4|-\left(-2\right)^{0}$$

Cancel out 2 and 2.

$$\frac{28}{27}-\sqrt{3}\sqrt{3}+|-4|-\left(-2\right)^{0}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{28}{27}-3+|-4|-\left(-2\right)^{0}$$

Subtract 3 from \frac{28}{27} to get -\frac{53}{27}.

$$-\frac{53}{27}+|-4|-\left(-2\right)^{0}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -4 is 4.

$$-\frac{53}{27}+4-\left(-2\right)^{0}$$

Add -\frac{53}{27} and 4 to get \frac{55}{27}.

$$\frac{55}{27}-\left(-2\right)^{0}$$

Calculate -2 to the power of 0 and get 1.

$$\frac{55}{27}-1$$

Subtract 1 from \frac{55}{27} to get \frac{28}{27}.

$$\frac{28}{27}$$