Question

How do you simplify `\frac { 5^ { - 5} } { 5^ { 8} }`?

Answer 1

See the entire simplification process below:

Explanation:

The first rule of exponents we will use is:

`x^color(red)(a) = 1/x^color(red)(-a)`

`5^color(red)(-5)/5^8 = 1/(5^color(red)(- -5) * 5^8) = 1/(5^5 * 5^8)`

The next rule of exponents to use is:

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

`1/(5^color(red)(5) * 5^color(blue)(8)) = 1/(5^(color(red)(5)+color(blue)(8))) = 1/5^13 = 1/(1,220,703,125)`