Respuesta :

MrGumby

Answer:

In this problem, the answer is n = 3

Step-by-step explanation:

Since we are just looking for what the exponent "n" on the q in the middle is, we can really ignore each p and r. They will not affect the equation at all since we are only dealing with the q terms. This leaves us with this below.

q^2 * q^n = q^5

Since we add together exponents when multiplying we know.

2 + n = 5

And using basic algebra, we can tell that n = 3

gmany

[tex]p^3\cdot q^2\left(\dfrac{p^4\cdot q^n\cdot r^3}{r^{-4}}\right)=p^7q^5r^7\\\\Use:\ a^n\cdot a^m=a^{n+m},\ \dfrac{a^n}{a^m}=a^{n-m}\\\\p^{3+4}q^{2+n}r^{3-(-4)}=p^7q^5r^7\\\\p^7q^{2+n}r^7=p^7q^5r^7\to q^{2+n}=q^5\to2+n=5\qquad\text{subtract 2 from both sides}\\\\\boxed{n=3}[/tex]

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