Question

In a polynomials equation do you add the exponents if they are different

Answer 1

You can only add exponents if you are multiplying two of the same variable together. For example,
$x^{12} \times x^4 = x^{16}$

You take them away if you are dividing.
$x^{12} \div x^4 = x^{8}$

In a polynomial equation, you can add together two of the same variable if they have the same exponent
$3x^4 + 7x^4 = 10x^4$

Or you can take them away in a similar fashion,
$3x^4 - 7x^4 = -4x^4$

But you cannot add two (or more) different exponents,
$6+4x+7x^2 = 6+4x+7x^2$ (it does not get any simpler)

I hope this has answered your question, if not, leave a comment and I'll update the answer.