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

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

Evaluate

$$500$$

Solution Steps

Calculate 5 to the power of 3 and get 125.

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

Calculate 25 to the power of 2 and get 625.

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

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

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

Calculate 8 to the power of 2 and get 64.

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

Calculate 4 to the power of 2 and get 16.

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

Divide 64 by 16 to get 4.

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

Calculate 4 to the power of 3 and get 64.

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

Multiply \frac{1}{5} and 64 to get \frac{64}{5}.

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

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

$$\frac{64}{5}\times \frac{625}{16}$$

Multiply \frac{64}{5} and \frac{625}{16} to get 500.

$$500$$

Factor

$$2^{2}\times 5^{3}$$