Question

How do you simplify `(64n^12)^(-1/6)`?

Answer 1

See the entire simplification process below:

Explanation:

First, we will use these rule of exponents to start the simplification process:

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

`a = a^color(red)(1)`

`(64n^color(red)(12))^(color(blue)(-1/6)) = (64^color(red)(1)n^color(red)(12))^(color(blue)(-1/6)) =`

`64^(color(red)(1) xx color(blue)(-1/6))n^(color(red)(12) xx color(blue)(-1/6)) = 64^(-1/6)n^-2`

Now we can use this rule for exponents to continue the simplification process:

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

`64^(-1/6)n^-2 = 1/(64^(- -1/6)n^(- -2)) = 1/(64^(1/6)n^2)`

Now, to finish we need to know `2^6 = 64` and `(-2)^6 = 64` therefore `64^(1/6) = 2` or `-2`

`1/(64^(1/6)n^2) = 1/(2n^2)` or `1/(64^(1/6)n^2) = -1/(2n^2)`