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

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Answer 1 · 2017-04-17T23:57:56

$(hm)/g$

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

Answer 2 · 2017-04-17T23:58:09

See the entire solution process below:

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:

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

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

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