Simplify `(9g^2h^8)/(6g^5h^4)`

One method is to write as the product of three monomials:

`(9/6)(g^2/g^5)(h^8/h^4)` .

Now `9/6=3/2`

`g^2/g^5=1/g^3` . You can use the quotients rule with the negative exponent rule: `g^2/g^5=g^(2-5)=g^(-3)=1/g^3` .

You could change the division into a multiplication and use the product rule: `g^2/g^5=g^2*g^(-5)=g^(-3)=1/g^3`

Or you could use the definition of an exponent and cancel: `g^2/g^5=(g*g)/(g*g*g*g*g)=1/g^3`

Also `h^8/h^4=h^4` using similar reasoning.

Thus `(9g^2h^8)/(6g^5h^4)=(9/6)(g^2/g^5)(h^8/h^4)=(3/2)(1/g^3)(h^4/1)=(3h^4)/(2g^3)`

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**The simplified form is** `(3h^4)/(2g^3)`

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