Question

P^3×q^2(p^4×q^n×r^3/r^-4)=p^7q^5r^7

What does n=

Answer 1

`n = 3`

Explanation:

Given:

The equation given is:

`p^3q^2(p^4q^n* (r^3)/(r^(-4)))=p^7q^5r^7`

We simplify the given equation using the following law of indices:

`a^m* a^n=a^(m+n)\\(a^m)/(a^n)=a^(m-n)`

Therefore,

`p^(3+4)q^(n+2)* r^(3-(-4)))=p^7q^5r^7\\p^7q^(n+2)r^7=p^7q^5r^7\\q^(n+2)=q^5`

Since the base on both the sides is same, therefore, their exponents must also be same. This gives,

`n+2=5\\n=5-2\\n=3`

Therefore, the value of 'n' is 3.