I assume you're trying to simplify these.
For all of these, divide the coefficients separately from the x's and that separately from the y's.
#5: [tex]\dfrac{16t^4}{8t}[/tex]
Start with 16/8 = 2.
Then move to [tex]\dfrac{t^4}{t}[/tex].
[tex]\dfrac{t^4}{t} = \dfrac{t \cdot t \cdot t \cdot t}{t}[/tex]
So, you'll cancel out one t from the top with the one t in the bottom and be left with [tex]t^3[/tex].
Putting that all together:
[tex]\dfrac{16t^4}{8t} = 2t^3[/tex]
#6: [tex]\dfrac{x^6y^{14}}{x^4y^9}[/tex]
You have 6 x's in the top and 4 x's in the bottom. When you cancel out 4 from the top to cancel the 4 in the bottom, you'll be left with 2 x's in the top:
[tex]\dfrac{x^6}{x^4}=x^2[/tex]
Similarly, 14 y's up top and 9 in the bottom. When you cancel one-for-one, you'll be left with 5 y's up top:
[tex]\dfrac{y^{14}}{y^9}=y^5[/tex]
Putting that all together:
[tex]\dfrac{x^6y^{14}}{x^4y^9}=x^2y^5[/tex]
#7: [tex]\dfrac{3^4x^4}{3x^2}[/tex]
This is the same as #6, just with 3's and x's.
You have four 3's up top and one in the bottom. When you cancel, you'll be left with three 3's up top:
[tex]\dfrac{3^4}{3}=3^3[/tex]
You have 4 x's up top and 2 x's down below. That will leave 2 x's up top once you cancel them out:
[tex]\dfrac{x^4}{x^2}=x^2[/tex]
Putting that together:
[tex]\dfrac{3^4x^4}{3x^2}=3^3x^2[/tex]
