Question

What is the division property of exponents?

Answer 1

Answer:

$\dfrac{a^b}{a^c}=a^{(b-c)}$

Step-by-step explanation:

An exponent represents repeated multiplication. For example, ...

... x^3 = x·x·x

... x^2 = x·x

If we divide these, the x's in the denominator cancel an equal number in the numerator:

... (x·x·x)/(x·x) = x

If we represent the repeated multiplication using exponents, we can represent the cancellation by subtraction:

... (x^3)/(x^2) = x^(3-2) = x^1 = x

Once we have this idea in mind that division can be done by subtracting denominator exponents, we can use it regardless of the magnitude or sign of the exponents involved.