Solve -3^2+3^33^5/3^6/{3^2}+{left(frac{1/5right)}^-1}{{left(6/8right)}^-1}-frac{10sqrt{178}}{{178}^}

$$- { 3 }^{ 2 } + \frac{ \frac{ { 3 }^{ 3 } { 3 }^{ 5 } }{ { 3 }^{ 6 } } }{ { 3 }^{ 2 } } + \frac{ { \left( \frac{ 1 }{ 5 } \right) }^{ -1 } }{ { \left( \frac{ 6 }{ 8 } \right) }^{ -1 } } - \frac{ 10 \sqrt{ 178 } }{ { 178 }^{ } }$$

Evaluate

$$-\frac{5\sqrt{178}}{89}-\frac{17}{4}\approx -4.999531689$$

Short Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$-3^{2}+\frac{\frac{3^{8}}{3^{6}}}{3^{2}}+\frac{\left(\frac{1}{5}\right)^{-1}}{\left(\frac{6}{8}\right)^{-1}}-\frac{10\sqrt{178}}{178^{1}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 6 from 8 to get 2.

$$-3^{2}+\frac{3^{2}}{3^{2}}+\frac{\left(\frac{1}{5}\right)^{-1}}{\left(\frac{6}{8}\right)^{-1}}-\frac{10\sqrt{178}}{178^{1}}$$

Divide 3^{2} by 3^{2} to get 1.

$$-3^{2}+1+\frac{\left(\frac{1}{5}\right)^{-1}}{\left(\frac{6}{8}\right)^{-1}}-\frac{10\sqrt{178}}{178^{1}}$$

Calculate 3 to the power of 2 and get 9.

$$-9+1+\frac{\left(\frac{1}{5}\right)^{-1}}{\left(\frac{6}{8}\right)^{-1}}-\frac{10\sqrt{178}}{178^{1}}$$

Add -9 and 1 to get -8.

$$-8+\frac{\left(\frac{1}{5}\right)^{-1}}{\left(\frac{6}{8}\right)^{-1}}-\frac{10\sqrt{178}}{178^{1}}$$

Calculate \frac{1}{5} to the power of -1 and get 5.

$$-8+\frac{5}{\left(\frac{6}{8}\right)^{-1}}-\frac{10\sqrt{178}}{178^{1}}$$

Reduce the fraction \frac{6}{8} to lowest terms by extracting and canceling out 2.

$$-8+\frac{5}{\left(\frac{3}{4}\right)^{-1}}-\frac{10\sqrt{178}}{178^{1}}$$

Calculate \frac{3}{4} to the power of -1 and get \frac{4}{3}.

$$-8+\frac{5}{\frac{4}{3}}-\frac{10\sqrt{178}}{178^{1}}$$

Divide 5 by \frac{4}{3} by multiplying 5 by the reciprocal of \frac{4}{3}.

$$-8+5\times \frac{3}{4}-\frac{10\sqrt{178}}{178^{1}}$$

Multiply 5 and \frac{3}{4} to get \frac{15}{4}.

$$-8+\frac{15}{4}-\frac{10\sqrt{178}}{178^{1}}$$

Add -8 and \frac{15}{4} to get -\frac{17}{4}.

$$-\frac{17}{4}-\frac{10\sqrt{178}}{178^{1}}$$

Cancel out 2 in both numerator and denominator.

$$-\frac{17}{4}-\frac{5\sqrt{178}}{89}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 89 is 356. Multiply -\frac{17}{4} times \frac{89}{89}. Multiply \frac{5\sqrt{178}}{89} times \frac{4}{4}.

$$-\frac{17\times 89}{356}-\frac{4\times 5\sqrt{178}}{356}$$

Since -\frac{17\times 89}{356} and \frac{4\times 5\sqrt{178}}{356} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-17\times 89-4\times 5\sqrt{178}}{356}$$

Do the multiplications in -17\times 89-4\times 5\sqrt{178}.

$$\frac{-1513-20\sqrt{178}}{356}$$

Factor

$$\frac{-20 \sqrt{178} - 1513}{356} = -4.999531688995861$$