What is what to do when adding exponents?

When adding exponents, it's crucial to remember that you can only directly add terms if they have the same base and the same exponent.

  • If the bases and exponents are the same: Treat the exponential term as a common factor. For instance, 2x² + 3x² = (2+3)x² = 5x². You simply add the coefficients (the numbers in front of the exponential term) and keep the base and exponent the same.

  • If the bases are the same but the exponents are different: You cannot directly add them. For example, x² + x³ cannot be simplified further.

  • If the bases are different: Again, you cannot directly add them. For example, 2² + 3² cannot be combined directly. You would need to calculate each term separately and then add the results: 4 + 9 = 13.

In summary, direct addition of exponents is only permissible when the bases and exponents are identical. Otherwise, the expression might need to be evaluated directly or require other algebraic manipulations depending on the problem.