Question

What is the simplified form of 18g^6h^6 over 12g^9h^4 ?

Answer 1

Hint:\[\frac{18 g^6h^6}{12g^9h^4} = \frac{18}{12}g^6g^{\color{red}{-9}}h^6h^{\color{red}{-4}}\]

Answer 2

Factoring numerator (top) and denominator( bottom) \[\frac{18g^6h^6 }{ 12g^9 h^4 }=\frac{(3)(6)}{(2)(6)}\frac{g^6}{g^9} \frac{h^6 }{ h^4 }\] you can write the original expression as the above product.
Next use a rule for exponents \[\frac{a^n}{a^m}=a^na^{-m}=a^{n-m}\]
and you should get \[\frac{3}{2}\frac{1}{g^3}\frac{h^2}{1}\] or \[\frac{3h^2}{2g^3}\]