Solve -frac{41}3^3-(-1)^3/3

$$- \frac { 41 } { 3 } ^ { 3 } - \frac { ( - 1 ) ^ { 3 } } { 3 }$$

Evaluate

$$-\frac{68912}{27}\approx -2552.296296296$$

Solution Steps

Calculate \frac{41}{3} to the power of 3 and get \frac{68921}{27}.

$$-\frac{68921}{27}-\frac{\left(-1\right)^{3}}{3}$$

Calculate -1 to the power of 3 and get -1.

$$-\frac{68921}{27}-\frac{-1}{3}$$

Fraction \frac{-1}{3} can be rewritten as -\frac{1}{3} by extracting the negative sign.

$$-\frac{68921}{27}-\left(-\frac{1}{3}\right)$$

The opposite of -\frac{1}{3} is \frac{1}{3}.

$$-\frac{68921}{27}+\frac{1}{3}$$

Least common multiple of 27 and 3 is 27. Convert -\frac{68921}{27} and \frac{1}{3} to fractions with denominator 27.

$$-\frac{68921}{27}+\frac{9}{27}$$

Since -\frac{68921}{27} and \frac{9}{27} have the same denominator, add them by adding their numerators.

$$\frac{-68921+9}{27}$$

Add -68921 and 9 to get -68912.

$$-\frac{68912}{27}$$

Factor

$$-\frac{68912}{27} = -2552\frac{8}{27} = -2552.296296296296$$