Question

How do you evaluate and simplify `9/9^(-4/5)`?

Answer 1

See a solution process below:

Explanation:

First, use this rule of exponents to eliminate the negative exponent:

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

`9/9^color(red)(-4/5) = 9 * 9^color(red)(- -4/5) = 9 * 9^(4/5)`

Next, use these rules to combine the 9's terms:

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

`9 * 9^(4/5) => 9^color(red)(1) * 9^color(blue)(4/5) => 9^(color(red)(1)+color(blue)(4/5)) => 9^(color(red)(5/5)+color(blue)(4/5)) =>`

`9^(9/5)`

Answer 2

`:.color(blue)(=52.196` to the nearest 3 decimal places

Explanation:

`9/(1/9^(-4/5))`

`:.1/a^-2=a^2`

`:.=9/(1/9^(4/5))`

`:.=9/1 xx 9^(4/5)/1`

`:.=9^(5/5) xx 9^(4/5)`

`:.=9^(9/5)`

`:.=root5(9^9)`

`:.=root5(9*9*9*9*9*9*9*9*9)`

`:.root5(9)*root5(9)*root5(9)*root5(9)*root5(9)=9`

`:.=9root5(9*9*9*9)`

`:.=9root5(3*3*3*3*3*3*3*3)`

`:.root5(3)*root5(3)*root5(3)*root5(3)*root5(3)=3`

`:.=3*9root5(27)`

`:.=27root5(27)`

`:.=52.19591521`

`:.color(blue)(=52.196` to the nearest 3 decimal places