Solve {l}{3/4(-8)-(-2/3)^{2}+(1/2)^3(-10)-2/5(-frac{1}{2})(-frac{10}{3})(-2)^2+}{+frac{1}{6}(-1)^5(-3)+sqrt{25}-(frac{1}{6})^234}

$$\left. \begin{array} { l } { \frac { 3 } { 4 } ( - 8 ) - ( - \frac { 2 } { 3 } ) ^ { 2 } + ( \frac { 1 } { 2 } ) ^ { 3 } ( - 10 ) - \frac { 2 } { 5 } ( - \frac { 1 } { 2 } ) ( - \frac { 10 } { 3 } ) ( - 2 ) ^ { 2 } + } \\ { + \frac { 1 } { 6 } ( - 1 ) ^ { 5 } ( - 3 ) + \sqrt { 25 } - ( \frac { 1 } { 6 } ) ^ { 2 } 34 } \end{array} \right.$$

Evaluate

$$-\frac{209}{36}\approx -5.805555556$$

Solution Steps

Express \frac{3}{4}\left(-8\right) as a single fraction.

$$\frac{3\left(-8\right)}{4}-\left(-\frac{2}{3}\right)^{2}+\left(\frac{1}{2}\right)^{3}\left(-10\right)-\frac{2}{5}\left(-\frac{1}{2}\right)\left(-\frac{10}{3}\right)\left(-2\right)^{2}+\frac{1}{6}\left(-1\right)^{5}\left(-3\right)+\sqrt{25}-\left(\frac{1}{6}\right)^{2}\times 34$$

Multiply 3 and -8 to get -24.

$$\frac{-24}{4}-\left(-\frac{2}{3}\right)^{2}+\left(\frac{1}{2}\right)^{3}\left(-10\right)-\frac{2}{5}\left(-\frac{1}{2}\right)\left(-\frac{10}{3}\right)\left(-2\right)^{2}+\frac{1}{6}\left(-1\right)^{5}\left(-3\right)+\sqrt{25}-\left(\frac{1}{6}\right)^{2}\times 34$$

Divide -24 by 4 to get -6.

$$-6-\left(-\frac{2}{3}\right)^{2}+\left(\frac{1}{2}\right)^{3}\left(-10\right)-\frac{2}{5}\left(-\frac{1}{2}\right)\left(-\frac{10}{3}\right)\left(-2\right)^{2}+\frac{1}{6}\left(-1\right)^{5}\left(-3\right)+\sqrt{25}-\left(\frac{1}{6}\right)^{2}\times 34$$

Calculate -\frac{2}{3} to the power of 2 and get \frac{4}{9}.

$$-6-\frac{4}{9}+\left(\frac{1}{2}\right)^{3}\left(-10\right)-\frac{2}{5}\left(-\frac{1}{2}\right)\left(-\frac{10}{3}\right)\left(-2\right)^{2}+\frac{1}{6}\left(-1\right)^{5}\left(-3\right)+\sqrt{25}-\left(\frac{1}{6}\right)^{2}\times 34$$

Convert -6 to fraction -\frac{54}{9}.

$$-\frac{54}{9}-\frac{4}{9}+\left(\frac{1}{2}\right)^{3}\left(-10\right)-\frac{2}{5}\left(-\frac{1}{2}\right)\left(-\frac{10}{3}\right)\left(-2\right)^{2}+\frac{1}{6}\left(-1\right)^{5}\left(-3\right)+\sqrt{25}-\left(\frac{1}{6}\right)^{2}\times 34$$

Since -\frac{54}{9} and \frac{4}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-54-4}{9}+\left(\frac{1}{2}\right)^{3}\left(-10\right)-\frac{2}{5}\left(-\frac{1}{2}\right)\left(-\frac{10}{3}\right)\left(-2\right)^{2}+\frac{1}{6}\left(-1\right)^{5}\left(-3\right)+\sqrt{25}-\left(\frac{1}{6}\right)^{2}\times 34$$

Subtract 4 from -54 to get -58.

$$-\frac{58}{9}+\left(\frac{1}{2}\right)^{3}\left(-10\right)-\frac{2}{5}\left(-\frac{1}{2}\right)\left(-\frac{10}{3}\right)\left(-2\right)^{2}+\frac{1}{6}\left(-1\right)^{5}\left(-3\right)+\sqrt{25}-\left(\frac{1}{6}\right)^{2}\times 34$$

Calculate \frac{1}{2} to the power of 3 and get \frac{1}{8}.

$$-\frac{58}{9}+\frac{1}{8}\left(-10\right)-\frac{2}{5}\left(-\frac{1}{2}\right)\left(-\frac{10}{3}\right)\left(-2\right)^{2}+\frac{1}{6}\left(-1\right)^{5}\left(-3\right)+\sqrt{25}-\left(\frac{1}{6}\right)^{2}\times 34$$

Multiply \frac{1}{8} and -10 to get \frac{-10}{8}.

$$-\frac{58}{9}+\frac{-10}{8}-\frac{2}{5}\left(-\frac{1}{2}\right)\left(-\frac{10}{3}\right)\left(-2\right)^{2}+\frac{1}{6}\left(-1\right)^{5}\left(-3\right)+\sqrt{25}-\left(\frac{1}{6}\right)^{2}\times 34$$

Reduce the fraction \frac{-10}{8} to lowest terms by extracting and canceling out 2.

$$-\frac{58}{9}-\frac{5}{4}-\frac{2}{5}\left(-\frac{1}{2}\right)\left(-\frac{10}{3}\right)\left(-2\right)^{2}+\frac{1}{6}\left(-1\right)^{5}\left(-3\right)+\sqrt{25}-\left(\frac{1}{6}\right)^{2}\times 34$$

Least common multiple of 9 and 4 is 36. Convert -\frac{58}{9} and \frac{5}{4} to fractions with denominator 36.

$$-\frac{232}{36}-\frac{45}{36}-\frac{2}{5}\left(-\frac{1}{2}\right)\left(-\frac{10}{3}\right)\left(-2\right)^{2}+\frac{1}{6}\left(-1\right)^{5}\left(-3\right)+\sqrt{25}-\left(\frac{1}{6}\right)^{2}\times 34$$

Since -\frac{232}{36} and \frac{45}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-232-45}{36}-\frac{2}{5}\left(-\frac{1}{2}\right)\left(-\frac{10}{3}\right)\left(-2\right)^{2}+\frac{1}{6}\left(-1\right)^{5}\left(-3\right)+\sqrt{25}-\left(\frac{1}{6}\right)^{2}\times 34$$

Subtract 45 from -232 to get -277.

$$-\frac{277}{36}-\frac{2}{5}\left(-\frac{1}{2}\right)\left(-\frac{10}{3}\right)\left(-2\right)^{2}+\frac{1}{6}\left(-1\right)^{5}\left(-3\right)+\sqrt{25}-\left(\frac{1}{6}\right)^{2}\times 34$$

Multiply \frac{2}{5} times -\frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{277}{36}-\frac{2\left(-1\right)}{5\times 2}\left(-\frac{10}{3}\right)\left(-2\right)^{2}+\frac{1}{6}\left(-1\right)^{5}\left(-3\right)+\sqrt{25}-\left(\frac{1}{6}\right)^{2}\times 34$$

Cancel out 2 in both numerator and denominator.

$$-\frac{277}{36}-\frac{-1}{5}\left(-\frac{10}{3}\right)\left(-2\right)^{2}+\frac{1}{6}\left(-1\right)^{5}\left(-3\right)+\sqrt{25}-\left(\frac{1}{6}\right)^{2}\times 34$$

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

$$-\frac{277}{36}-\left(-\frac{1}{5}\left(-\frac{10}{3}\right)\left(-2\right)^{2}\right)+\frac{1}{6}\left(-1\right)^{5}\left(-3\right)+\sqrt{25}-\left(\frac{1}{6}\right)^{2}\times 34$$

Multiply -\frac{1}{5} times -\frac{10}{3} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{277}{36}-\frac{-\left(-10\right)}{5\times 3}\left(-2\right)^{2}+\frac{1}{6}\left(-1\right)^{5}\left(-3\right)+\sqrt{25}-\left(\frac{1}{6}\right)^{2}\times 34$$

Do the multiplications in the fraction \frac{-\left(-10\right)}{5\times 3}.

$$-\frac{277}{36}-\frac{10}{15}\left(-2\right)^{2}+\frac{1}{6}\left(-1\right)^{5}\left(-3\right)+\sqrt{25}-\left(\frac{1}{6}\right)^{2}\times 34$$

Reduce the fraction \frac{10}{15} to lowest terms by extracting and canceling out 5.

$$-\frac{277}{36}-\frac{2}{3}\left(-2\right)^{2}+\frac{1}{6}\left(-1\right)^{5}\left(-3\right)+\sqrt{25}-\left(\frac{1}{6}\right)^{2}\times 34$$

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

$$-\frac{277}{36}-\frac{2}{3}\times 4+\frac{1}{6}\left(-1\right)^{5}\left(-3\right)+\sqrt{25}-\left(\frac{1}{6}\right)^{2}\times 34$$

Express \frac{2}{3}\times 4 as a single fraction.

$$-\frac{277}{36}-\frac{2\times 4}{3}+\frac{1}{6}\left(-1\right)^{5}\left(-3\right)+\sqrt{25}-\left(\frac{1}{6}\right)^{2}\times 34$$

Multiply 2 and 4 to get 8.

$$-\frac{277}{36}-\frac{8}{3}+\frac{1}{6}\left(-1\right)^{5}\left(-3\right)+\sqrt{25}-\left(\frac{1}{6}\right)^{2}\times 34$$

Least common multiple of 36 and 3 is 36. Convert -\frac{277}{36} and \frac{8}{3} to fractions with denominator 36.

$$-\frac{277}{36}-\frac{96}{36}+\frac{1}{6}\left(-1\right)^{5}\left(-3\right)+\sqrt{25}-\left(\frac{1}{6}\right)^{2}\times 34$$

Since -\frac{277}{36} and \frac{96}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-277-96}{36}+\frac{1}{6}\left(-1\right)^{5}\left(-3\right)+\sqrt{25}-\left(\frac{1}{6}\right)^{2}\times 34$$

Subtract 96 from -277 to get -373.

$$-\frac{373}{36}+\frac{1}{6}\left(-1\right)^{5}\left(-3\right)+\sqrt{25}-\left(\frac{1}{6}\right)^{2}\times 34$$

Calculate -1 to the power of 5 and get -1.

$$-\frac{373}{36}+\frac{1}{6}\left(-1\right)\left(-3\right)+\sqrt{25}-\left(\frac{1}{6}\right)^{2}\times 34$$

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

$$-\frac{373}{36}-\frac{1}{6}\left(-3\right)+\sqrt{25}-\left(\frac{1}{6}\right)^{2}\times 34$$

Express -\frac{1}{6}\left(-3\right) as a single fraction.

$$-\frac{373}{36}+\frac{-\left(-3\right)}{6}+\sqrt{25}-\left(\frac{1}{6}\right)^{2}\times 34$$

Multiply -1 and -3 to get 3.

$$-\frac{373}{36}+\frac{3}{6}+\sqrt{25}-\left(\frac{1}{6}\right)^{2}\times 34$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$-\frac{373}{36}+\frac{1}{2}+\sqrt{25}-\left(\frac{1}{6}\right)^{2}\times 34$$

Least common multiple of 36 and 2 is 36. Convert -\frac{373}{36} and \frac{1}{2} to fractions with denominator 36.

$$-\frac{373}{36}+\frac{18}{36}+\sqrt{25}-\left(\frac{1}{6}\right)^{2}\times 34$$

Since -\frac{373}{36} and \frac{18}{36} have the same denominator, add them by adding their numerators.

$$\frac{-373+18}{36}+\sqrt{25}-\left(\frac{1}{6}\right)^{2}\times 34$$

Add -373 and 18 to get -355.

$$-\frac{355}{36}+\sqrt{25}-\left(\frac{1}{6}\right)^{2}\times 34$$

Calculate the square root of 25 and get 5.

$$-\frac{355}{36}+5-\left(\frac{1}{6}\right)^{2}\times 34$$

Convert 5 to fraction \frac{180}{36}.

$$-\frac{355}{36}+\frac{180}{36}-\left(\frac{1}{6}\right)^{2}\times 34$$

Since -\frac{355}{36} and \frac{180}{36} have the same denominator, add them by adding their numerators.

$$\frac{-355+180}{36}-\left(\frac{1}{6}\right)^{2}\times 34$$

Add -355 and 180 to get -175.

$$-\frac{175}{36}-\left(\frac{1}{6}\right)^{2}\times 34$$

Calculate \frac{1}{6} to the power of 2 and get \frac{1}{36}.

$$-\frac{175}{36}-\frac{1}{36}\times 34$$

Multiply \frac{1}{36} and 34 to get \frac{34}{36}.

$$-\frac{175}{36}-\frac{34}{36}$$

Since -\frac{175}{36} and \frac{34}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-175-34}{36}$$

Subtract 34 from -175 to get -209.

$$-\frac{209}{36}$$

Factor

$$-\frac{209}{36} = -5\frac{29}{36} = -5.805555555555555$$