Solve {l}{(5/9)^10*(5/9)^10}{(1/5)^-2*5^2}

$$\left. \begin{array} { l } { ( \frac { 5 } { 9 } ) ^ { 10 } \cdot ( \frac { 5 } { 9 } ) ^ { 10 } } \\ { ( \frac { 1 } { 5 } ) ^ { - 2 } \cdot 5 ^ { 2 } } \end{array} \right.$$

Sort

$$\frac{95367431640625}{12157665459056928801},\ 625$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 10 and 10 to get 20.

$$sort(\left(\frac{5}{9}\right)^{20},\left(\frac{1}{5}\right)^{-2}\times 5^{2})$$

Calculate \frac{5}{9} to the power of 20 and get \frac{95367431640625}{12157665459056928801}.

$$sort(\frac{95367431640625}{12157665459056928801},\left(\frac{1}{5}\right)^{-2}\times 5^{2})$$

Calculate \frac{1}{5} to the power of -2 and get 25.

$$sort(\frac{95367431640625}{12157665459056928801},25\times 5^{2})$$

Calculate 5 to the power of 2 and get 25.

$$sort(\frac{95367431640625}{12157665459056928801},25\times 25)$$

Multiply 25 and 25 to get 625.

$$sort(\frac{95367431640625}{12157665459056928801},625)$$

Convert decimal numbers in the list \frac{95367431640625}{12157665459056928801},625 to fractions.

$$\frac{95367431640625}{12157665459056928801},625$$

Evaluate

$$\frac{95367431640625}{12157665459056928801},\ 625$$