Question

Why do you subtract exponents when dividing powers with the same base?

Answer 1

Let's see why that happens by evaluating an expression with exponents.


`(a^(20))/(a^(10))` <-- Now expand the exponent

`(a^(20))/(a^(10)) = ((a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a))/((a)(a)(a)(a)(a)(a)(a)(a)(a)(a))`

Now simplify the fraction by canceling out any common factors on the numerator and denominator.


`((a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a))/((a)(a)(a)(a)(a)(a)(a)(a)(a)(a)) = ((a)(a)(a)(a)(a)(a)(a)(a)(a)(a))/(1) = a^(10)`

So, it's the same thing as subtracting the powers.