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\frac{4\sqrt{5}}{3}\sqrt{\frac{1}{5}}\times \frac{5}{2}\sqrt{5}
Factor 80=4^{2}\times 5. Rewrite the square root of the product \sqrt{4^{2}\times 5} as the product of square roots \sqrt{4^{2}}\sqrt{5}. Take the square root of 4^{2}.
\frac{4\sqrt{5}}{3}\times \frac{\sqrt{1}}{\sqrt{5}}\times \frac{5}{2}\sqrt{5}
Rewrite the square root of the division \sqrt{\frac{1}{5}} as the division of square roots \frac{\sqrt{1}}{\sqrt{5}}.
\frac{4\sqrt{5}}{3}\times \frac{1}{\sqrt{5}}\times \frac{5}{2}\sqrt{5}
Calculate the square root of 1 and get 1.
\frac{4\sqrt{5}}{3}\times \frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\times \frac{5}{2}\sqrt{5}
Rationalize the denominator of \frac{1}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.
\frac{4\sqrt{5}}{3}\times \frac{\sqrt{5}}{5}\times \frac{5}{2}\sqrt{5}
The square of \sqrt{5} is 5.
\frac{4\sqrt{5}\sqrt{5}}{3\times 5}\times \frac{5}{2}\sqrt{5}
Multiply \frac{4\sqrt{5}}{3} times \frac{\sqrt{5}}{5} by multiplying numerator times numerator and denominator times denominator.
\frac{4\sqrt{5}\sqrt{5}\times 5}{3\times 5\times 2}\sqrt{5}
Multiply \frac{4\sqrt{5}\sqrt{5}}{3\times 5} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.
\frac{2\sqrt{5}\sqrt{5}}{3}\sqrt{5}
Cancel out 2\times 5 in both numerator and denominator.
\frac{2\sqrt{5}\sqrt{5}\sqrt{5}}{3}
Express \frac{2\sqrt{5}\sqrt{5}}{3}\sqrt{5} as a single fraction.
\frac{2\times 5\sqrt{5}}{3}
Multiply \sqrt{5} and \sqrt{5} to get 5.
\frac{10\sqrt{5}}{3}
Multiply 2 and 5 to get 10.