Question

How do you simplify `(f^-3g^5h^8)^-3` and write it using only positive exponents?

Answer 1

See the entire simplification process below:

Explanation:

First use this rule of exponents to remove the exponent outside the parenthesis:

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

`(f^color(red)(-3)g^color(red)(5)h^color(red)(8))^color(blue)(-3) = f^(color(red)(-3) xx color(blue)(-3))g^(color(red)(5) xx color(blue)(-3))h^(color(red)(8) xx color(blue)(-3)) = f^9g^(-15)h^(-24)`

Now, we can use this rule of exponents to remove the negative exponents:
`x^color(red)(a) = 1/x^color(red)(-a)`

`f^9g^color(red)(-15)h^color(red)(-24) = f^9/g^color(red)(--15)h^color(red)(- -24) = f^9/g^15h^24`