Question

How do you simplify `\frac { ( 9s ) ^ { 5} } { ( 9s ) ^ { 10} }`?

Answer 1

See the entire solution process below:

Explanation:

First, use this rule of exponents to simplify the numerator and denominator:

`(9s)^color(red)(5)/(9s)^color(blue)(10) = 1/(9s)^(color(blue)(10)-color(red)(5)) = 1/(9s)^5`

Now, use these two rules of exponents to complete the simplification:

`a = a^color(red)(1)` and `(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))`

`1/(9s)^5 = 1/((9^color(red)(1)s^color(red)(1))^color(blue)(5)) = 1/(9^(color(red)(1) xx color(blue)(5))s^(color(red)(1) xx color(blue)(5))) = 1/(9^5s^5) = 1/(59049s^5)`