You cannot directly subtract exponents when the bases are different.
To understand why, let's first clarify what we mean by "subtracting exponents." Subtraction of exponents is a specific rule that applies when you are dividing terms with the same base, not when you are trying to subtract terms with different bases. This means that you can’t perform simple exponent subtraction between two separate terms that have different bases (for example, 23 - 32). Here's a breakdown of the concept:
Understanding the Limitations
As the provided reference states, in order to add or subtract variables with exponents, you need to have **like bases and like exponents**. This means that not only do the bases need to be the same, but the exponents need to be the same too to combine terms by adding or subtracting. In your case, since you have different bases, exponent subtraction doesn't apply.
What You Can Do
When you encounter terms with different bases and exponents, you cannot simply subtract the exponents. Instead, the recommended approach is:
- Evaluate each term: Calculate the value of each exponential expression individually.
- Perform the subtraction: After evaluating, subtract the numerical results as regular numbers.
Example
Let's consider the expression 53 - 24:
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Evaluate 53: 53 = 5 * 5 * 5 = 125
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Evaluate 24: 24 = 2 * 2 * 2 * 2 = 16
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Perform the subtraction: 125 - 16 = 109
So, 53 - 24 = 109
It’s important to remember that the rule of subtracting exponents (such as xm / xn = xm-n) is specifically for division when the bases are the same and doesn’t work for subtraction when bases are different, according to the reference.
Summary
In summary, you can’t subtract exponents directly if the bases are different. You need to evaluate each exponential term separately and then subtract the results. You can only subtract the exponents when the operation is division and the bases are equal.
