Solve (5/2)^10*[(5/4)^5]^-2

$$( \frac { 5 } { 2 } ) ^ { 10 } \cdot [ ( \frac { 5 } { 4 } ) ^ { 5 } ] ^ { - 2 }$$

Evaluate

$$1024$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 5 and -2 to get -10.

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

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

$$\frac{9765625}{1024}\times \left(\frac{5}{4}\right)^{-10}$$

Calculate \frac{5}{4} to the power of -10 and get \frac{1048576}{9765625}.

$$\frac{9765625}{1024}\times \frac{1048576}{9765625}$$

Multiply \frac{9765625}{1024} and \frac{1048576}{9765625} to get 1024.

$$1024$$

Factor

$$2^{10}$$