what is the exponent of 289

289 = 17^2

To find the exponent of 289, we need to determine what number must be raised to some power in order to equal 289. In this case, we want to find the exponent of 289 in the expression c^x = 289, where c is the base and x is the exponent.

To solve for x, we need to find a number whose exponent is equal to 289. We can start by trying different values of x, starting from 1 and increasing until we find a number that works.

Let's try some values:

- c^1 = 1 (not equal to 289)
- c^2 = 4 (not equal to 289)
- c^3 = 9 (not equal to 289)
- c^4 = 16 (not equal to 289)
- c^5 = 25 (not equal to 289)
- c^6 = 36 (not equal to 289)

Based on these values, we can see that 289 is not a perfect power of any integer up to 6. It means there is no integer exponent x that satisfies c^x = 289.

Therefore, we can conclude that there is no integer exponent for 289.