Solve -450^circ+7^5:7^5/(frac{2{3})^-2}-frac{6sqrt{31}}{-sqrt{11}}

$$\frac { - 450 ^ { \circ } + 7 ^ { 5 } : 7 ^ { 5 } } { ( \frac { 2 } { 3 } ) ^ { - 2 } } - \frac { 6 \sqrt { 31 } } { - \sqrt { 11 } }$$

Evaluate

$$\frac{6\sqrt{341}}{11}-\frac{1796}{9}\approx -189.48309084$$

Short Solution Steps

Divide 7^{5} by 7^{5} to get 1.

$$\frac{-450+1}{\left(\frac{2}{3}\right)^{-2}}-\frac{6\sqrt{31}}{-\sqrt{11}}$$

Add -450 and 1 to get -449.

$$\frac{-449}{\left(\frac{2}{3}\right)^{-2}}-\frac{6\sqrt{31}}{-\sqrt{11}}$$

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

$$\frac{-449}{\frac{9}{4}}-\frac{6\sqrt{31}}{-\sqrt{11}}$$

Divide -449 by \frac{9}{4} by multiplying -449 by the reciprocal of \frac{9}{4}.

$$-449\times \frac{4}{9}-\frac{6\sqrt{31}}{-\sqrt{11}}$$

Multiply -449 and \frac{4}{9} to get -\frac{1796}{9}.

$$-\frac{1796}{9}-\frac{6\sqrt{31}}{-\sqrt{11}}$$

Cancel out -1 in both numerator and denominator.

$$-\frac{1796}{9}-\frac{-6\sqrt{31}}{\sqrt{11}}$$

Rationalize the denominator of \frac{-6\sqrt{31}}{\sqrt{11}} by multiplying numerator and denominator by \sqrt{11}.

$$-\frac{1796}{9}-\frac{-6\sqrt{31}\sqrt{11}}{\left(\sqrt{11}\right)^{2}}$$

The square of \sqrt{11} is 11.

$$-\frac{1796}{9}-\frac{-6\sqrt{31}\sqrt{11}}{11}$$

To multiply \sqrt{31} and \sqrt{11}, multiply the numbers under the square root.

$$-\frac{1796}{9}-\frac{-6\sqrt{341}}{11}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 9 and 11 is 99. Multiply -\frac{1796}{9} times \frac{11}{11}. Multiply \frac{-6\sqrt{341}}{11} times \frac{9}{9}.

$$-\frac{1796\times 11}{99}-\frac{9\left(-6\right)\sqrt{341}}{99}$$

Since -\frac{1796\times 11}{99} and \frac{9\left(-6\right)\sqrt{341}}{99} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-1796\times 11-9\left(-6\right)\sqrt{341}}{99}$$

Do the multiplications in -1796\times 11-9\left(-6\right)\sqrt{341}.

$$\frac{-19756+54\sqrt{341}}{99}$$

Factor

$$\frac{2 {(27 \sqrt{341} - 9878)}}{99} = -189.48309083958134$$