Question

How do you simplify `(p ^ { 5} q ^ { - 11} ) ^ { 10}`?

Answer 1

See a solution process below:

Explanation:

First, we can use this rule for exponents to eliminate the outer exponent:

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

`(p^color(red)(5)q^color(red)(-11))^color(blue)(10) => p^(color(red)(5) xx color(blue)(10))q^(color(red)(-11) xx color(blue)(10)) => p^50q^-110`

Now, we can use this rule of exponents to eliminate the negative exponent:

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

`p^50q^color(red)(-110) => p^50/q^color(red)(- -110) => p^50/q^color(red)(110)`