Answer:
[tex]n = 3[/tex]
Step-by-step explanation:
Given:
The equation given is:
[tex]p^3q^2(p^4q^n\times \frac{r^3}{r^{-4}})=p^7q^5r^7[/tex]
We simplify the given equation using the following law of indices:
[tex]a^m\times a^n=a^{m+n}\\\frac{a^m}{a^n}=a^{m-n}[/tex]
Therefore,
[tex]p^{3+4}q^{n+2}\times r^{3-(-4)})=p^7q^5r^7\\p^7q^{n+2}r^7=p^7q^5r^7\\q^{n+2}=q^5[/tex]
Since the base on both the sides is same, therefore, their exponents must also be same. This gives,
[tex]n+2=5\\n=5-2\\n=3[/tex]
Therefore, the value of 'n' is 3.
