Solve left(66^2right)^2sqrt{5/2+3/5(4/6){left(5/5right)}^-2}

$${ \left(6 { 6 }^{ 2 } \right) }^{ 2 } \sqrt{ \frac{ 5 }{ 2 } + \frac{ 3 }{ 5 } ( \frac{ 4 }{ 6 } ) { \left( \frac{ 5 }{ 5 } \right) }^{ -2 } }$$

Evaluate

$$\frac{23328\sqrt{290}}{5}\approx 79452.305028866$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\left(6^{3}\right)^{2}\sqrt{\frac{5}{2}+\frac{3}{5}\times \frac{4}{6}\times \left(\frac{5}{5}\right)^{-2}}$$

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

$$6^{6}\sqrt{\frac{5}{2}+\frac{3}{5}\times \frac{4}{6}\times \left(\frac{5}{5}\right)^{-2}}$$

Divide 5 by 5 to get 1.

$$6^{6}\sqrt{\frac{5}{2}+\frac{3}{5}\times \frac{4}{6}\times 1^{-2}}$$

Calculate 6 to the power of 6 and get 46656.

$$46656\sqrt{\frac{5}{2}+\frac{3}{5}\times \frac{4}{6}\times 1^{-2}}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$46656\sqrt{\frac{5}{2}+\frac{3}{5}\times \frac{2}{3}\times 1^{-2}}$$

Multiply \frac{3}{5} and \frac{2}{3} to get \frac{2}{5}.

$$46656\sqrt{\frac{5}{2}+\frac{2}{5}\times 1^{-2}}$$

Calculate 1 to the power of -2 and get 1.

$$46656\sqrt{\frac{5}{2}+\frac{2}{5}\times 1}$$

Multiply \frac{2}{5} and 1 to get \frac{2}{5}.

$$46656\sqrt{\frac{5}{2}+\frac{2}{5}}$$

Add \frac{5}{2} and \frac{2}{5} to get \frac{29}{10}.

$$46656\sqrt{\frac{29}{10}}$$

Rewrite the square root of the division \sqrt{\frac{29}{10}} as the division of square roots \frac{\sqrt{29}}{\sqrt{10}}.

$$46656\times \frac{\sqrt{29}}{\sqrt{10}}$$

Rationalize the denominator of \frac{\sqrt{29}}{\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$46656\times \frac{\sqrt{29}\sqrt{10}}{\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$46656\times \frac{\sqrt{29}\sqrt{10}}{10}$$

To multiply \sqrt{29} and \sqrt{10}, multiply the numbers under the square root.

$$46656\times \frac{\sqrt{290}}{10}$$

Express 46656\times \frac{\sqrt{290}}{10} as a single fraction.

$$\frac{46656\sqrt{290}}{10}$$

Divide 46656\sqrt{290} by 10 to get \frac{23328}{5}\sqrt{290}.

$$\frac{23328}{5}\sqrt{290}$$