Solve 23-4^3/108+(-19)^3-1/15=

$$\frac { 23 - 4 ^ { 3 } } { 108 } + ( - 19 ) ^ { 3 } - \frac { 1 } { 15 } =$$

Evaluate

$$-\frac{3704101}{540}\approx -6859.446296296$$

Solution Steps

Calculate 4 to the power of 3 and get 64.

$$\frac{23-64}{108}+\left(-19\right)^{3}-\frac{1}{15}$$

Subtract 64 from 23 to get -41.

$$\frac{-41}{108}+\left(-19\right)^{3}-\frac{1}{15}$$

Fraction \frac{-41}{108} can be rewritten as -\frac{41}{108} by extracting the negative sign.

$$-\frac{41}{108}+\left(-19\right)^{3}-\frac{1}{15}$$

Calculate -19 to the power of 3 and get -6859.

$$-\frac{41}{108}-6859-\frac{1}{15}$$

Convert 6859 to fraction \frac{740772}{108}.

$$-\frac{41}{108}-\frac{740772}{108}-\frac{1}{15}$$

Since -\frac{41}{108} and \frac{740772}{108} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-41-740772}{108}-\frac{1}{15}$$

Subtract 740772 from -41 to get -740813.

$$-\frac{740813}{108}-\frac{1}{15}$$

Least common multiple of 108 and 15 is 540. Convert -\frac{740813}{108} and \frac{1}{15} to fractions with denominator 540.

$$-\frac{3704065}{540}-\frac{36}{540}$$

Since -\frac{3704065}{540} and \frac{36}{540} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-3704065-36}{540}$$

Subtract 36 from -3704065 to get -3704101.

$$-\frac{3704101}{540}$$

Factor

$$-\frac{3704101}{540} = -6859\frac{241}{540} = -6859.446296296296$$