Solve 2^5/5-2^3/3-2(2)^2-4(2)-[-1/5+1/3-2+4]

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

Evaluate

$$-\frac{72}{5}=-14.4$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

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

Calculate 2 to the power of 5 and get 32.

$$\frac{32}{5}-\frac{2^{3}}{3}-2^{3}-4\times 2-\left(\frac{-1}{5}+\frac{1}{3}-2+4\right)$$

Calculate 2 to the power of 3 and get 8.

$$\frac{32}{5}-\frac{8}{3}-2^{3}-4\times 2-\left(\frac{-1}{5}+\frac{1}{3}-2+4\right)$$

Least common multiple of 5 and 3 is 15. Convert \frac{32}{5} and \frac{8}{3} to fractions with denominator 15.

$$\frac{96}{15}-\frac{40}{15}-2^{3}-4\times 2-\left(\frac{-1}{5}+\frac{1}{3}-2+4\right)$$

Since \frac{96}{15} and \frac{40}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{96-40}{15}-2^{3}-4\times 2-\left(\frac{-1}{5}+\frac{1}{3}-2+4\right)$$

Subtract 40 from 96 to get 56.

$$\frac{56}{15}-2^{3}-4\times 2-\left(\frac{-1}{5}+\frac{1}{3}-2+4\right)$$

Calculate 2 to the power of 3 and get 8.

$$\frac{56}{15}-8-4\times 2-\left(\frac{-1}{5}+\frac{1}{3}-2+4\right)$$

Convert 8 to fraction \frac{120}{15}.

$$\frac{56}{15}-\frac{120}{15}-4\times 2-\left(\frac{-1}{5}+\frac{1}{3}-2+4\right)$$

Since \frac{56}{15} and \frac{120}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{56-120}{15}-4\times 2-\left(\frac{-1}{5}+\frac{1}{3}-2+4\right)$$

Subtract 120 from 56 to get -64.

$$-\frac{64}{15}-4\times 2-\left(\frac{-1}{5}+\frac{1}{3}-2+4\right)$$

Multiply 4 and 2 to get 8.

$$-\frac{64}{15}-8-\left(\frac{-1}{5}+\frac{1}{3}-2+4\right)$$

Convert 8 to fraction \frac{120}{15}.

$$-\frac{64}{15}-\frac{120}{15}-\left(\frac{-1}{5}+\frac{1}{3}-2+4\right)$$

Since -\frac{64}{15} and \frac{120}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-64-120}{15}-\left(\frac{-1}{5}+\frac{1}{3}-2+4\right)$$

Subtract 120 from -64 to get -184.

$$-\frac{184}{15}-\left(\frac{-1}{5}+\frac{1}{3}-2+4\right)$$

Fraction \frac{-1}{5} can be rewritten as -\frac{1}{5} by extracting the negative sign.

$$-\frac{184}{15}-\left(-\frac{1}{5}+\frac{1}{3}-2+4\right)$$

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

$$-\frac{184}{15}-\left(-\frac{3}{15}+\frac{5}{15}-2+4\right)$$

Since -\frac{3}{15} and \frac{5}{15} have the same denominator, add them by adding their numerators.

$$-\frac{184}{15}-\left(\frac{-3+5}{15}-2+4\right)$$

Add -3 and 5 to get 2.

$$-\frac{184}{15}-\left(\frac{2}{15}-2+4\right)$$

Convert 2 to fraction \frac{30}{15}.

$$-\frac{184}{15}-\left(\frac{2}{15}-\frac{30}{15}+4\right)$$

Since \frac{2}{15} and \frac{30}{15} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{184}{15}-\left(\frac{2-30}{15}+4\right)$$

Subtract 30 from 2 to get -28.

$$-\frac{184}{15}-\left(-\frac{28}{15}+4\right)$$

Convert 4 to fraction \frac{60}{15}.

$$-\frac{184}{15}-\left(-\frac{28}{15}+\frac{60}{15}\right)$$

Since -\frac{28}{15} and \frac{60}{15} have the same denominator, add them by adding their numerators.

$$-\frac{184}{15}-\frac{-28+60}{15}$$

Add -28 and 60 to get 32.

$$-\frac{184}{15}-\frac{32}{15}$$

Since -\frac{184}{15} and \frac{32}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-184-32}{15}$$

Subtract 32 from -184 to get -216.

$$\frac{-216}{15}$$

Reduce the fraction \frac{-216}{15} to lowest terms by extracting and canceling out 3.

$$-\frac{72}{5}$$

Factor

$$-\frac{72}{5} = -14\frac{2}{5} = -14.4$$