Help with adding exponents?

Question

how do add exponents with same bases but with different powers: eg: 3^5+3^6. please show me how to do so.

Answer 1

First of all, you can only add exponents that do have the same base. So you keep the base the same (3) and just simply add the exponents (11). The final answer will be 3^11. Hope this helps

Answer 2

You don't!  If you were multiplying then 3^5(3^6)= 3^11

to show why you can't add the exponents when adding try this.

Let x=2      x^3 + x^4 does not equal x^7 because

                 2^3 + 2^4= 2(2)2 + 2(2)(2)2= 8 +16 =24 DOES not equal 2^7 which is 2(2)(2)(2)(2)(2)2=128

        

Answer 3

You can't add them, any more than you can add x and x^2, and for exactly the same reason.

Let's look at what you have.  There's a common factor of 3^5, so let's factor it out:

3^5 + 3^6 = 3^5(1 + 3) = 4(3^5)

This is clearly very different from 3^11.  There is no general rule for adding exponents when the bases are the same, unless you mean something like:

(x^a)(x^b) = x^(a + b)

You'd have to have

(3^5)(3^6)  = 3^11