Yes, when dividing variable expressions with like bases, it is appropriate to subtract the exponents. This is known as the quotient property of exponents. It states that for any positive real numbers a and b, and any nonzero integers m and n, am ÷ an = am-n.
Here are some examples of how to apply the quotient property of exponents:
- x^5 ÷ x^2 = x^(5-2) = x^3.
- y^7 ÷ y^3 = y^(7-3) = y^4.
- z^10 ÷ z^4 = z^(10-4) = z^6.
The quotient property of exponents is a useful tool for simplifying algebraic expressions. It can also be used to solve equations that involve exponents.