You cannot directly multiply exponents when the bases are different; instead, you must calculate each exponential term separately and then multiply the resulting values.
Understanding the Process
When faced with multiplying exponents that have different bases, remember this fundamental rule: you cannot combine them directly. The expression 23 * 32 is not equal to 65, for example. Here's the breakdown:
-
Calculate Each Exponential Term Individually: Expand each exponential term by multiplying the base by itself the number of times indicated by the exponent.
- For example, 23 becomes 2 2 2.
- Similarly, 32 becomes 3 * 3.
-
Multiply the Results: After calculating each exponential term, multiply the results together to get the final answer.
Example
Let's take the expression 23 * 32 as an example to illustrate:
| Step | Calculation | Result |
|---|---|---|
| Expand 23 | 2 2 2 | 8 |
| Expand 32 | 3 * 3 | 9 |
| Multiply results | 8 * 9 | 72 |
Therefore, 23 * 32 = 72
Additional Examples
-
*52 23**
- 52 = 5 * 5 = 25
- 23 = 2 2 2 = 8
- 25 * 8 = 200
-
*41 33**
- 41 = 4
- 33 = 3 3 3 = 27
- 4 * 27 = 108
Key Takeaway
To multiply exponents with different bases, you have to:
- Expand each exponential term into a series of multiplications.
- Perform the multiplication for each term.
- Multiply the resulting values from each term together to get the final answer.
As stated in the reference "Multiplying exponents when the bases are different", you must calculate each exponential term and then multiply the resulting values.
