Question

How do you simplify `(g^6h^2m)/(hg^7)`?

Answer 1

`(hm)/g`

Explanation:

`(g^6h^2m)/hg^7 = g^6/g^7*h^2/h*m = 1/g*h*m=(hm)/g`

Answer 2

See the entire solution process below:

Explanation:

First, use this rule of exponents to modify the `h` term in the denominator:

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

`(g^6h^2m)/(hg^7) = (g^6h^2m)/(h^color(blue)(1)g^7)`

Next, use these rules of exponents to simplify the `g` and `h` terms in the numerator and denominator:

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

`(g^6h^2m)/(h^color(red)(1)g^7) = (h^(color(red)(2)-color(blue)(1))m)/g^(color(blue)(7)-color(red)(6)) = (h^1m)/g^1`

Now, we can use the reverse of the first rule to finalize the simplification:

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

`(h^1 m)/(g^1) = (hm)/g`