Solve (1/3(1)^{3}-2(1)^2+4(1)-1/5(1)^5)-(1/3(-2)^3-2(-2)^2+4(-2)-1/6(-2))

$$( \frac { 1 } { 3 } ( 1 ) ^ { 3 } - 2 ( 1 ) ^ { 2 } + 4 ( 1 ) - \frac { 1 } { 5 } ( 1 ) ^ { 5 } ) - ( \frac { 1 } { 3 } ( - 2 ) ^ { 3 } - 2 ( - 2 ) ^ { 2 } + 4 ( - 2 ) - \frac { 1 } { 6 } ( - 2 ) )$$

Evaluate

$$\frac{307}{15}\approx 20.466666667$$

Solution Steps

Calculate 1 to the power of 3 and get 1.

$$\frac{1}{3}\times 1-2\times 1^{2}+4\times 1-\frac{1}{5}\times 1^{5}-\left(\frac{1}{3}\left(-2\right)^{3}-2\left(-2\right)^{2}+4\left(-2\right)-\frac{1}{6}\left(-2\right)\right)$$

Multiply \frac{1}{3} and 1 to get \frac{1}{3}.

$$\frac{1}{3}-2\times 1^{2}+4\times 1-\frac{1}{5}\times 1^{5}-\left(\frac{1}{3}\left(-2\right)^{3}-2\left(-2\right)^{2}+4\left(-2\right)-\frac{1}{6}\left(-2\right)\right)$$

Calculate 1 to the power of 2 and get 1.

$$\frac{1}{3}-2\times 1+4\times 1-\frac{1}{5}\times 1^{5}-\left(\frac{1}{3}\left(-2\right)^{3}-2\left(-2\right)^{2}+4\left(-2\right)-\frac{1}{6}\left(-2\right)\right)$$

Multiply 2 and 1 to get 2.

$$\frac{1}{3}-2+4\times 1-\frac{1}{5}\times 1^{5}-\left(\frac{1}{3}\left(-2\right)^{3}-2\left(-2\right)^{2}+4\left(-2\right)-\frac{1}{6}\left(-2\right)\right)$$

Convert 2 to fraction \frac{6}{3}.

$$\frac{1}{3}-\frac{6}{3}+4\times 1-\frac{1}{5}\times 1^{5}-\left(\frac{1}{3}\left(-2\right)^{3}-2\left(-2\right)^{2}+4\left(-2\right)-\frac{1}{6}\left(-2\right)\right)$$

Since \frac{1}{3} and \frac{6}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-6}{3}+4\times 1-\frac{1}{5}\times 1^{5}-\left(\frac{1}{3}\left(-2\right)^{3}-2\left(-2\right)^{2}+4\left(-2\right)-\frac{1}{6}\left(-2\right)\right)$$

Subtract 6 from 1 to get -5.

$$-\frac{5}{3}+4\times 1-\frac{1}{5}\times 1^{5}-\left(\frac{1}{3}\left(-2\right)^{3}-2\left(-2\right)^{2}+4\left(-2\right)-\frac{1}{6}\left(-2\right)\right)$$

Multiply 4 and 1 to get 4.

$$-\frac{5}{3}+4-\frac{1}{5}\times 1^{5}-\left(\frac{1}{3}\left(-2\right)^{3}-2\left(-2\right)^{2}+4\left(-2\right)-\frac{1}{6}\left(-2\right)\right)$$

Convert 4 to fraction \frac{12}{3}.

$$-\frac{5}{3}+\frac{12}{3}-\frac{1}{5}\times 1^{5}-\left(\frac{1}{3}\left(-2\right)^{3}-2\left(-2\right)^{2}+4\left(-2\right)-\frac{1}{6}\left(-2\right)\right)$$

Since -\frac{5}{3} and \frac{12}{3} have the same denominator, add them by adding their numerators.

$$\frac{-5+12}{3}-\frac{1}{5}\times 1^{5}-\left(\frac{1}{3}\left(-2\right)^{3}-2\left(-2\right)^{2}+4\left(-2\right)-\frac{1}{6}\left(-2\right)\right)$$

Add -5 and 12 to get 7.

$$\frac{7}{3}-\frac{1}{5}\times 1^{5}-\left(\frac{1}{3}\left(-2\right)^{3}-2\left(-2\right)^{2}+4\left(-2\right)-\frac{1}{6}\left(-2\right)\right)$$

Calculate 1 to the power of 5 and get 1.

$$\frac{7}{3}-\frac{1}{5}\times 1-\left(\frac{1}{3}\left(-2\right)^{3}-2\left(-2\right)^{2}+4\left(-2\right)-\frac{1}{6}\left(-2\right)\right)$$

Multiply \frac{1}{5} and 1 to get \frac{1}{5}.

$$\frac{7}{3}-\frac{1}{5}-\left(\frac{1}{3}\left(-2\right)^{3}-2\left(-2\right)^{2}+4\left(-2\right)-\frac{1}{6}\left(-2\right)\right)$$

Least common multiple of 3 and 5 is 15. Convert \frac{7}{3} and \frac{1}{5} to fractions with denominator 15.

$$\frac{35}{15}-\frac{3}{15}-\left(\frac{1}{3}\left(-2\right)^{3}-2\left(-2\right)^{2}+4\left(-2\right)-\frac{1}{6}\left(-2\right)\right)$$

Since \frac{35}{15} and \frac{3}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{35-3}{15}-\left(\frac{1}{3}\left(-2\right)^{3}-2\left(-2\right)^{2}+4\left(-2\right)-\frac{1}{6}\left(-2\right)\right)$$

Subtract 3 from 35 to get 32.

$$\frac{32}{15}-\left(\frac{1}{3}\left(-2\right)^{3}-2\left(-2\right)^{2}+4\left(-2\right)-\frac{1}{6}\left(-2\right)\right)$$

Calculate -2 to the power of 3 and get -8.

$$\frac{32}{15}-\left(\frac{1}{3}\left(-8\right)-2\left(-2\right)^{2}+4\left(-2\right)-\frac{1}{6}\left(-2\right)\right)$$

Multiply \frac{1}{3} and -8 to get \frac{-8}{3}.

$$\frac{32}{15}-\left(\frac{-8}{3}-2\left(-2\right)^{2}+4\left(-2\right)-\frac{1}{6}\left(-2\right)\right)$$

Fraction \frac{-8}{3} can be rewritten as -\frac{8}{3} by extracting the negative sign.

$$\frac{32}{15}-\left(-\frac{8}{3}-2\left(-2\right)^{2}+4\left(-2\right)-\frac{1}{6}\left(-2\right)\right)$$

Calculate -2 to the power of 2 and get 4.

$$\frac{32}{15}-\left(-\frac{8}{3}-2\times 4+4\left(-2\right)-\frac{1}{6}\left(-2\right)\right)$$

Multiply 2 and 4 to get 8.

$$\frac{32}{15}-\left(-\frac{8}{3}-8+4\left(-2\right)-\frac{1}{6}\left(-2\right)\right)$$

Convert 8 to fraction \frac{24}{3}.

$$\frac{32}{15}-\left(-\frac{8}{3}-\frac{24}{3}+4\left(-2\right)-\frac{1}{6}\left(-2\right)\right)$$

Since -\frac{8}{3} and \frac{24}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{32}{15}-\left(\frac{-8-24}{3}+4\left(-2\right)-\frac{1}{6}\left(-2\right)\right)$$

Subtract 24 from -8 to get -32.

$$\frac{32}{15}-\left(-\frac{32}{3}+4\left(-2\right)-\frac{1}{6}\left(-2\right)\right)$$

Multiply 4 and -2 to get -8.

$$\frac{32}{15}-\left(-\frac{32}{3}-8-\frac{1}{6}\left(-2\right)\right)$$

Convert 8 to fraction \frac{24}{3}.

$$\frac{32}{15}-\left(-\frac{32}{3}-\frac{24}{3}-\frac{1}{6}\left(-2\right)\right)$$

Since -\frac{32}{3} and \frac{24}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{32}{15}-\left(\frac{-32-24}{3}-\frac{1}{6}\left(-2\right)\right)$$

Subtract 24 from -32 to get -56.

$$\frac{32}{15}-\left(-\frac{56}{3}-\frac{1}{6}\left(-2\right)\right)$$

Multiply \frac{1}{6} and -2 to get \frac{-2}{6}.

$$\frac{32}{15}-\left(-\frac{56}{3}-\frac{-2}{6}\right)$$

Reduce the fraction \frac{-2}{6} to lowest terms by extracting and canceling out 2.

$$\frac{32}{15}-\left(-\frac{56}{3}-\left(-\frac{1}{3}\right)\right)$$

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

$$\frac{32}{15}-\left(-\frac{56}{3}+\frac{1}{3}\right)$$

Since -\frac{56}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

$$\frac{32}{15}-\frac{-56+1}{3}$$

Add -56 and 1 to get -55.

$$\frac{32}{15}-\left(-\frac{55}{3}\right)$$

The opposite of -\frac{55}{3} is \frac{55}{3}.

$$\frac{32}{15}+\frac{55}{3}$$

Least common multiple of 15 and 3 is 15. Convert \frac{32}{15} and \frac{55}{3} to fractions with denominator 15.

$$\frac{32}{15}+\frac{275}{15}$$

Since \frac{32}{15} and \frac{275}{15} have the same denominator, add them by adding their numerators.

$$\frac{32+275}{15}$$

Add 32 and 275 to get 307.

$$\frac{307}{15}$$

Factor

$$\frac{307}{3 \cdot 5} = 20\frac{7}{15} = 20.466666666666665$$