Question

How do you simplify the expression `(5g^4h^-3)^-3` using the properties?

Answer 1

See the entire simplification process below:

Explanation:

First, use these rules of exponents to simplify the outer exponent:

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

`(5g^4h^-3)^-3 = (5^color(red)(1)g^color(red)(4)h^color(red)(-3))^color(blue)(-3) = 5^(color(red)(1)xxcolor(blue)(-3))g^(color(red)(4)xxcolor(blue)(-3))h^(color(red)(-3)xxcolor(blue)(-3)) =`

`5^-3g^-12h^9`

To simplify this for expression with no negative exponents use the following rule of exponents:

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

`5^color(red)(-3)g^color(red)(-12)h^9 = h^9/(5^color(red)(- -3)g^color(red)(- -12)) = h^9/(5^3g^12) = h^9/(125g^12)`