Solve (frac{5^{3}}{25^{2}})^{2}*(8^2/4^2)^3*(5/2)^4

$$( \frac { 5 ^ { 3 } } { 25 ^ { 2 } } ) ^ { 2 } \times ( \frac { 8 ^ { 2 } } { 4 ^ { 2 } } ) ^ { 3 } \times ( \frac { 5 } { 2 } ) ^ { 4 }$$

Evaluate

$$100$$

Solution Steps

Calculate 5 to the power of 3 and get 125.

$$\left(\frac{125}{25^{2}}\right)^{2}\times \left(\frac{8^{2}}{4^{2}}\right)^{3}\times \left(\frac{5}{2}\right)^{4}$$

Calculate 25 to the power of 2 and get 625.

$$\left(\frac{125}{625}\right)^{2}\times \left(\frac{8^{2}}{4^{2}}\right)^{3}\times \left(\frac{5}{2}\right)^{4}$$

Reduce the fraction \frac{125}{625} to lowest terms by extracting and canceling out 125.

$$\left(\frac{1}{5}\right)^{2}\times \left(\frac{8^{2}}{4^{2}}\right)^{3}\times \left(\frac{5}{2}\right)^{4}$$

Calculate \frac{1}{5} to the power of 2 and get \frac{1}{25}.

$$\frac{1}{25}\times \left(\frac{8^{2}}{4^{2}}\right)^{3}\times \left(\frac{5}{2}\right)^{4}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{1}{25}\times \left(\frac{64}{4^{2}}\right)^{3}\times \left(\frac{5}{2}\right)^{4}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{1}{25}\times \left(\frac{64}{16}\right)^{3}\times \left(\frac{5}{2}\right)^{4}$$

Divide 64 by 16 to get 4.

$$\frac{1}{25}\times 4^{3}\times \left(\frac{5}{2}\right)^{4}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{1}{25}\times 64\times \left(\frac{5}{2}\right)^{4}$$

Multiply \frac{1}{25} and 64 to get \frac{64}{25}.

$$\frac{64}{25}\times \left(\frac{5}{2}\right)^{4}$$

Calculate \frac{5}{2} to the power of 4 and get \frac{625}{16}.

$$\frac{64}{25}\times \frac{625}{16}$$

Multiply \frac{64}{25} and \frac{625}{16} to get 100.

$$100$$

Factor

$$2^{2}\times 5^{2}$$