Question

Help me on this algebra please

Answer 1

`p^3\cdot q^2\left((p^4\cdot q^n\cdot r^3)/(r^(-4))\right)=p^7q^5r^7\\\\Use:\ a^n\cdot a^m=a^(n+m),\ (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}`

Answer 2

In this problem, the answer is n = 3

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