Solve (25/4)^2*(5/3)^2*(frac{sqrt{5}}{5})^2=

$$( \frac { 25 } { 4 } ) ^ { 2 } \times ( \frac { 5 } { 3 } ) ^ { 2 } \times ( \frac { \sqrt { 5 } } { 5 } ) ^ { 2 } =$$

Evaluate

$$\frac{3125}{144}\approx 21.701388889$$

Solution Steps

Calculate \frac{25}{4} to the power of 2 and get \frac{625}{16}.

$$\frac{625}{16}\times \left(\frac{5}{3}\right)^{2}\times \left(\frac{\sqrt{5}}{5}\right)^{2}$$

Calculate \frac{5}{3} to the power of 2 and get \frac{25}{9}.

$$\frac{625}{16}\times \frac{25}{9}\times \left(\frac{\sqrt{5}}{5}\right)^{2}$$

Multiply \frac{625}{16} and \frac{25}{9} to get \frac{15625}{144}.

$$\frac{15625}{144}\times \left(\frac{\sqrt{5}}{5}\right)^{2}$$

To raise \frac{\sqrt{5}}{5} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{15625}{144}\times \frac{\left(\sqrt{5}\right)^{2}}{5^{2}}$$

Multiply \frac{15625}{144} times \frac{\left(\sqrt{5}\right)^{2}}{5^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{15625\left(\sqrt{5}\right)^{2}}{144\times 5^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{15625\times 5}{144\times 5^{2}}$$

Multiply 15625 and 5 to get 78125.

$$\frac{78125}{144\times 5^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{78125}{144\times 25}$$

Multiply 144 and 25 to get 3600.

$$\frac{78125}{3600}$$

Reduce the fraction \frac{78125}{3600} to lowest terms by extracting and canceling out 25.

$$\frac{3125}{144}$$

Factor

$$\frac{5 ^ {5}}{2 ^ {4} \cdot 3 ^ {2}} = 21\frac{101}{144} = 21.70138888888889$$