To subtract exponents with variables, you first need to ensure you are dealing with the same base. When dividing terms with the same base, you subtract the exponents. When subtracting exponential expressions, the terms must have like bases and like exponents.
Dividing Terms with the Same Base
The main situation where you "subtract exponents" involving variables is during division.
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Rule: xm / xn = xm-n
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Explanation: When dividing terms with the same base (x), you subtract the exponent in the denominator (n) from the exponent in the numerator (m).
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Example:
- y5 / y2 = y5-2 = y3
Subtracting Exponential Expressions
If you're subtracting entire exponential expressions, it's a different process:
Requirements
According to the provided reference, to subtract exponential expressions with variables, you must have like bases and like exponents. This means you can only subtract terms that are identical except for their coefficients. You can then subtract the coefficients.
Process
- Identify Like Terms: Look for terms with the same variable raised to the same power (like bases and like exponents).
- Subtract Coefficients: Subtract the coefficients of the like terms. The variable and exponent remain the same.
Examples
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Example 1: Subtracting Like Terms
5x2 - 2x2 = (5-2)x2 = 3x2
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Example 2: No Subtraction Possible
5x2 - 2x3 (Cannot be simplified further because the exponents are different.)
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Example 3: Combining Like Terms Before Subtracting
(7a3 + 4b2) - (2a3 + b2) = 7a3 + 4b2 - 2a3 - b2 = (7a3 - 2a3) + (4b2 - b2) = 5a3 + 3b2
