Question

What is the value of n in the equation below a^n/a^3=a^9

Answer 1

One way in which you could do this problem quickly and accurately would be to mult. both sides by a^3, to elim. the fraction:

a^n = a^9 * a^3 = a^(9+3)  = a^12.    Thus, n = 12.

Answer 2

Answer: 12

Step-by-step explanation:

The given equation : $\frac{a^n}{a^3}=a^9$...........................(1)

According to the division law of exponent,

$\frac{x^m}{x^r}=x^{m-r}$

Therefore, $\frac{a^n}{a^3}=a^{n-3}$...................................(2)

From equation (1) and (2), we have

$a^{n-3}=a^9$

Since, the base is same in both sides, therefore, the exponents must be same.

$\Rightarrow n-3=9\\\\\Rightarrow\ n=9+3=12$

Hence, the value of n = 12.