Solve (14^-2/5)*sqrt{14/5}

$$( \frac{ { 14 }^{ -2 } }{ 5 } ) \times \sqrt{ \frac{ 14 }{ 5 } }$$

Evaluate

$$\frac{\sqrt{70}}{4900}\approx 0.001707469$$

Solution Steps

Calculate 14 to the power of -2 and get \frac{1}{196}.

$$\frac{\frac{1}{196}}{5}\sqrt{\frac{14}{5}}$$

Express \frac{\frac{1}{196}}{5} as a single fraction.

$$\frac{1}{196\times 5}\sqrt{\frac{14}{5}}$$

Multiply 196 and 5 to get 980.

$$\frac{1}{980}\sqrt{\frac{14}{5}}$$

Rewrite the square root of the division \sqrt{\frac{14}{5}} as the division of square roots \frac{\sqrt{14}}{\sqrt{5}}.

$$\frac{1}{980}\times \frac{\sqrt{14}}{\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{14}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{1}{980}\times \frac{\sqrt{14}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{1}{980}\times \frac{\sqrt{14}\sqrt{5}}{5}$$

To multiply \sqrt{14} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{1}{980}\times \frac{\sqrt{70}}{5}$$

Multiply \frac{1}{980} times \frac{\sqrt{70}}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\sqrt{70}}{980\times 5}$$

Multiply 980 and 5 to get 4900.

$$\frac{\sqrt{70}}{4900}$$