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

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

Evaluate

$$\frac{95367431640625}{1073741824}=88817.841970013$$

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{9765625}{1048576}.

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

Multiply \frac{9765625}{1024} and \frac{9765625}{1048576} to get \frac{95367431640625}{1073741824}.

$$\frac{95367431640625}{1073741824}$$

Factor

$$\frac{5 ^ {20}}{2 ^ {30}} = 88817\frac{904058417}{1073741824} = 88817.84197001252$$