When dealing with power in addition, it's essential to understand that you cannot directly add the exponents unless the bases are the same and you are dealing with identical terms. The provided reference explains a specific case where you have the same base and same exponent being added together.
Adding Identical Terms with Exponents
The reference highlights the following rule:
an + an = 2an
This rule applies only when you have identical terms with the same base a and the same exponent n. Essentially, you are adding one 'an' to another 'an', which results in two 'an's.
Here's a breakdown with examples:
- Understanding the Rule: The rule states that if you're adding two identical exponential expressions, you simply multiply the expression by 2.
- Example 1:
- 43 + 43 = 2(43)
- 2(43) = 2 (4 4 4) = 2 64 = 128
- Example 2:
- 52 + 52 = 2(52)
- 2(52) = 2 (5 5) = 2 * 25 = 50
- Example 3:
- 24 + 24 = 2(24)
- 2(24) = 2 (2 2 2 2) = 2 * 16 = 32
Key Considerations:
- Same Base and Exponent: The rule only applies if both terms being added have the same base and the same exponent.
- Different Bases or Exponents: If you have different bases (e.g., 23 + 33) or different exponents (e.g., 23 + 22) you cannot directly add the exponents or combine them using the provided rule. In such cases, you must evaluate each term individually and then add the results.
- Not Direct Exponent Addition: You do not directly add the exponents (i.e. it is not an + an = a2n).
Summary
In conclusion, when adding powers, you can only directly combine them into a multiplication expression when you are adding identical terms with the same base and the same exponent. The result is twice the original term (2*an) which can then be evaluated by solving the power of the base and then multiplying by 2.
