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

Explanation:

The given equation :
`(a^n)/(a^3)=a^9`...........................(1)

According to the division law of exponent,

`(x^m)/(x^r)=x^(m-r)`

Therefore,
`(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.