Simplify. Express your answer using positive exponents. (6fg^7h^5)(3f^3gh^3) f^4g^6h

To simplify the expression ((6fg^7h^5)(3f^3gh^3)) divided by (f^4g^6h), follow these steps:

1. Multiply the terms in the numerator:

[

(6 cdot 3)(f^{1 + 3})(g^{7 + 1})(h^{5 + 3}) = 18f^4g^8h^8

]

2. Set up the division:

Now we divide (18f^4g^8h^8) by (f^4g^6h):

[

frac{18f^4g^8h^8}{f^4g^6h}

]

3. Simplify the division:

– For (f):

[

frac{f^4}{f^4} = 1

]

– For (g):

[

frac{g^8}{g^6} = g^{8 – 6} = g^2

]

– For (h):

[

frac{h^8}{h^1} = h^{8 – 1} = h^7

]

4. Combine the results:

[

18g^2h^7