Answer: 12
Step-by-step explanation:
The given equation : [tex]\frac{a^n}{a^3}=a^9[/tex]...........................(1)
According to the division law of exponent,
[tex]\frac{x^m}{x^r}=x^{m-r}[/tex]
Therefore, [tex]\frac{a^n}{a^3}=a^{n-3}[/tex]...................................(2)
From equation (1) and (2), we have
[tex]a^{n-3}=a^9[/tex]
Since, the base is same in both sides, therefore, the exponents must be same.
[tex]\Rightarrow n-3=9\\\\\Rightarrow\ n=9+3=12[/tex]
Hence, the value of n = 12.
