Solve (25/4)^{2}*(2/5)^3*(8/125)^-3:[(2/5)^-1]^7

$$( \frac { 25 } { 4 } ) ^ { 2 } \cdot ( \frac { 2 } { 5 } ) ^ { 3 } \cdot ( \frac { 8 } { 125 } ) ^ { - 3 } : [ ( \frac { 2 } { 5 } ) ^ { - 1 } ] ^ { 7 }$$

Evaluate

$$\frac{125}{8}=15.625$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -1 and 7 to get -7.

$$\frac{\left(\frac{25}{4}\right)^{2}\times \left(\frac{2}{5}\right)^{3}\times \left(\frac{8}{125}\right)^{-3}}{\left(\frac{2}{5}\right)^{-7}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\left(\frac{8}{125}\right)^{-3}\times \left(\frac{2}{5}\right)^{10}\times \left(\frac{25}{4}\right)^{2}$$

Calculate \frac{8}{125} to the power of -3 and get \frac{1953125}{512}.

$$\frac{1953125}{512}\times \left(\frac{2}{5}\right)^{10}\times \left(\frac{25}{4}\right)^{2}$$

Calculate \frac{2}{5} to the power of 10 and get \frac{1024}{9765625}.

$$\frac{1953125}{512}\times \frac{1024}{9765625}\times \left(\frac{25}{4}\right)^{2}$$

Multiply \frac{1953125}{512} and \frac{1024}{9765625} to get \frac{2}{5}.

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

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

$$\frac{2}{5}\times \frac{625}{16}$$

Multiply \frac{2}{5} and \frac{625}{16} to get \frac{125}{8}.

$$\frac{125}{8}$$

Factor

$$\frac{5 ^ {3}}{2 ^ {3}} = 15\frac{5}{8} = 15.625$$