Solve -3^{2}+frac{3^{3}*3^{5}:3^{6}}{3^2}+(1/5)^-1/(frac{6{8})^-1}-frac{10sqrt{178}}{178^12}

$$- 3 ^ { 2 } + \frac { 3 ^ { 3 } \times 3 ^ { 5 } : 3 ^ { 6 } } { 3 ^ { 2 } } + \frac { ( \frac { 1 } { 5 } ) ^ { - 1 } } { ( \frac { 6 } { 8 } ) ^ { - 1 } } - \frac { 10 \sqrt { 178 } } { 178 ^ { 12 } }$$

Evaluate

$$-\frac{5\sqrt{178}}{505836346501656863341611008}-\frac{17}{4}\approx -4.25$$

Solution Steps

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

$$-3^{2}+\frac{\frac{3^{8}}{3^{6}}}{3^{2}}+\frac{\left(\frac{1}{5}\right)^{-1}}{\left(\frac{6}{8}\right)^{-1}}-\frac{10\sqrt{178}}{178^{12}}$$

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

$$-3^{2}+\frac{3^{2}}{3^{2}}+\frac{\left(\frac{1}{5}\right)^{-1}}{\left(\frac{6}{8}\right)^{-1}}-\frac{10\sqrt{178}}{178^{12}}$$

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

$$-3^{2}+1+\frac{\left(\frac{1}{5}\right)^{-1}}{\left(\frac{6}{8}\right)^{-1}}-\frac{10\sqrt{178}}{178^{12}}$$

Calculate 3 to the power of 2 and get 9.

$$-9+1+\frac{\left(\frac{1}{5}\right)^{-1}}{\left(\frac{6}{8}\right)^{-1}}-\frac{10\sqrt{178}}{178^{12}}$$

Add -9 and 1 to get -8.

$$-8+\frac{\left(\frac{1}{5}\right)^{-1}}{\left(\frac{6}{8}\right)^{-1}}-\frac{10\sqrt{178}}{178^{12}}$$

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

$$-8+\frac{5}{\left(\frac{6}{8}\right)^{-1}}-\frac{10\sqrt{178}}{178^{12}}$$

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

$$-8+\frac{5}{\left(\frac{3}{4}\right)^{-1}}-\frac{10\sqrt{178}}{178^{12}}$$

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

$$-8+\frac{5}{\frac{4}{3}}-\frac{10\sqrt{178}}{178^{12}}$$

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

$$-8+5\times \frac{3}{4}-\frac{10\sqrt{178}}{178^{12}}$$

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

$$-8+\frac{15}{4}-\frac{10\sqrt{178}}{178^{12}}$$

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

$$-\frac{17}{4}-\frac{10\sqrt{178}}{178^{12}}$$

Calculate 178 to the power of 12 and get 1011672693003313726683222016.

$$-\frac{17}{4}-\frac{10\sqrt{178}}{1011672693003313726683222016}$$

Divide 10\sqrt{178} by 1011672693003313726683222016 to get \frac{5}{505836346501656863341611008}\sqrt{178}.

$$-\frac{17}{4}-\frac{5}{505836346501656863341611008}\sqrt{178}$$

Factor

$$\frac{-5 \sqrt{178} - 2149804472632041669201846784}{505836346501656863341611008} = -4.25$$