It's important to understand that you cannot directly multiply exponents when the bases are different. The rule of adding exponents only applies when the bases are the same.
Understanding the Challenge
The reference Multiplying exponents with different bases states "First, multiply the bases together. Then, add the exponent." This is incorrect. You cannot simply add the exponents when the bases are different. Let's clarify how to handle this situation correctly.
Correct Approach to Multiplying with Different Bases
When multiplying terms with different bases and exponents, you cannot combine the exponents directly. Instead, you must:
- Evaluate each term individually: Calculate the value of each term with its specific base and exponent.
- Multiply the resulting values: After evaluating each term, multiply the results together.
Example
Let's consider a numerical example:
23 * 32
- Evaluate 23: 2 2 2 = 8
- Evaluate 32: 3 * 3 = 9
- Multiply the results: 8 * 9 = 72
Therefore, 23 * 32 = 72
When Can You Combine Exponents?
You can only combine exponents by adding them if the bases are the same. For instance, 23 * 22 = 2(3+2) = 25 = 32. This only works when the base is the same in the multiplication.
Common Mistakes to Avoid
- Incorrectly adding exponents: Do not try to add exponents if the bases are not identical. This is a common mistake as noted in the reference which incorrectly states that you add exponents when the bases are different.
- Confusing with power to a power: The rule (xa)b = xa*b is for when you have an exponent raised to another exponent. This rule does not apply to multiplication with different bases.
Summary
| Task | Action |
|---|---|
| Multiplying exponents with same base | Add the exponents. e.g., xa * xb = xa+b |
| Multiplying exponents with different bases | Evaluate each term separately, then multiply the resulting values. |
Remember, you must evaluate each exponential term individually and then perform the multiplication when bases are different.
