Solve -2^2/2(+1/3+2*3)-1)^-1+^10-

$$- \frac { 2 ^ { 2 } } { 2 } ( + \frac { 1 } { 3 } + 2 \cdot 3 ) - 1 ) ^ { - 1 } + ^ { 10 - }$$

Evaluate

$$-\frac{41}{3}\approx -13.666666667$$

Solution Steps

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

$$\left(-2^{1}\right)\left(\frac{1}{3}+2\times 3\right)-1$$

Calculate 2 to the power of 1 and get 2.

$$-2\left(\frac{1}{3}+2\times 3\right)-1$$

Multiply 2 and 3 to get 6.

$$-2\left(\frac{1}{3}+6\right)-1$$

Convert 6 to fraction \frac{18}{3}.

$$-2\left(\frac{1}{3}+\frac{18}{3}\right)-1$$

Since \frac{1}{3} and \frac{18}{3} have the same denominator, add them by adding their numerators.

$$-2\times \frac{1+18}{3}-1$$

Add 1 and 18 to get 19.

$$-2\times \frac{19}{3}-1$$

Express -2\times \frac{19}{3} as a single fraction.

$$\frac{-2\times 19}{3}-1$$

Multiply -2 and 19 to get -38.

$$\frac{-38}{3}-1$$

Fraction \frac{-38}{3} can be rewritten as -\frac{38}{3} by extracting the negative sign.

$$-\frac{38}{3}-1$$

Convert 1 to fraction \frac{3}{3}.

$$-\frac{38}{3}-\frac{3}{3}$$

Since -\frac{38}{3} and \frac{3}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-38-3}{3}$$

Subtract 3 from -38 to get -41.

$$-\frac{41}{3}$$

Factor

$$-\frac{41}{3} = -13\frac{2}{3} = -13.666666666666666$$