Solve (5/2)^0*[(5/4)^5]^-2

$$( \frac { 5 } { 2 } ) ^ { 0 } \cdot [ ( \frac { 5 } { 4 } ) ^ { 5 } ] ^ { - 2 }$$

Evaluate

$$\frac{1048576}{9765625}\approx 0.107374182$$

Solution Steps

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

$$\left(\frac{5}{2}\right)^{0}\times \left(\frac{5}{4}\right)^{-10}$$

Calculate \frac{5}{2} to the power of 0 and get 1.

$$1\times \left(\frac{5}{4}\right)^{-10}$$

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

$$1\times \frac{1048576}{9765625}$$

Multiply 1 and \frac{1048576}{9765625} to get \frac{1048576}{9765625}.

$$\frac{1048576}{9765625}$$

Factor

$$\frac{2 ^ {20}}{5 ^ {10}} = 0.1073741824$$