Solve 2*9/22sqrt{51116}52*left(46^2right)^3

$$2 \times \frac{ 9 }{ 22 \sqrt{ 51116 } } 52 \times { \left( { 46 }^{ 2 } \right) }^{ 3 }$$

Evaluate

$$\frac{170537344128\sqrt{12779}}{10813}\approx 1782878415.780838251$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$2\times 52\times \frac{9}{22\sqrt{51116}}\times 46^{6}$$

Multiply 2 and 52 to get 104.

$$104\times \frac{9}{22\sqrt{51116}}\times 46^{6}$$

Factor 51116=2^{2}\times 12779. Rewrite the square root of the product \sqrt{2^{2}\times 12779} as the product of square roots \sqrt{2^{2}}\sqrt{12779}. Take the square root of 2^{2}.

$$104\times \frac{9}{22\times 2\sqrt{12779}}\times 46^{6}$$

Multiply 22 and 2 to get 44.

$$104\times \frac{9}{44\sqrt{12779}}\times 46^{6}$$

Rationalize the denominator of \frac{9}{44\sqrt{12779}} by multiplying numerator and denominator by \sqrt{12779}.

$$104\times \frac{9\sqrt{12779}}{44\left(\sqrt{12779}\right)^{2}}\times 46^{6}$$

The square of \sqrt{12779} is 12779.

$$104\times \frac{9\sqrt{12779}}{44\times 12779}\times 46^{6}$$

Multiply 44 and 12779 to get 562276.

$$104\times \frac{9\sqrt{12779}}{562276}\times 46^{6}$$

Calculate 46 to the power of 6 and get 9474296896.

$$104\times \frac{9\sqrt{12779}}{562276}\times 9474296896$$

Multiply 104 and 9474296896 to get 985326877184.

$$985326877184\times \frac{9\sqrt{12779}}{562276}$$

Express 985326877184\times \frac{9\sqrt{12779}}{562276} as a single fraction.

$$\frac{985326877184\times 9\sqrt{12779}}{562276}$$

Multiply 985326877184 and 9 to get 8867941894656.

$$\frac{8867941894656\sqrt{12779}}{562276}$$

Divide 8867941894656\sqrt{12779} by 562276 to get \frac{170537344128}{10813}\sqrt{12779}.

$$\frac{170537344128}{10813}\sqrt{12779}$$