The provided question is slightly ambiguous. It can be interpreted in a couple of ways related to powers and subtraction:
Interpretation 1: Subtracting Terms with the Same Base and Exponent
This interpretation refers to situations where you're subtracting terms that have the same base raised to the same power. In this case, you subtract the coefficients of the terms, while the base and power remain unchanged.
According to the reference: To add and subtract powers, you must first ensure that the base and power of the two terms we use to add or subtract are the same. If they are the same, then you only have to add together their coefficients and let the base and power remain identical.
For example:
- 5x2 - 3x2 = (5 - 3)x2 = 2x2
Here, both terms have the same base x raised to the same power 2. We subtract the coefficients (5 and 3) and keep x2.
Interpretation 2: Subtracting Exponents When Dividing with the Same Base
This interpretation deals with the rule of exponents that states when dividing powers with the same base, you subtract the exponents. This is typically expressed as:
xm / xn = x(m-n)
In other words, when dividing two exponential terms with the same base, you keep the base and subtract the exponent of the denominator from the exponent of the numerator.
For example:
- x5 / x2 = x(5-2) = x3
Here, we divide two exponential terms with the same base (x), and thus, we simply subtract the exponent in the denominator(2) from the exponent in the numerator(5) and keep the base.
