This document discusses how to simplify exponential expressions when dividing numbers with the same base but different exponents. It provides examples of simplifying 37/33 and 53/58. The key rule explained is that when dividing numbers with the same base but different exponents, you copy the base and subtract the denominator's exponent from the numerator's exponent.

1. Dividing
Exponential
Expressions

2. Write
37
33 in expanded notation.
3 . 3 . 3 . 3 . 3 . 3 . 3
3 . 3 . 3
How do we simplify?
3 . 3 . 3 . 3 . 3 . 3 . 3
3 . 3 . 3
=
3 . 3 . 3
1
= 34

3. Write
53
58 in expanded notation.
5 . 5 . 5
5 . 5 . 5 . 5 . 5 . 5 . 5 . 5
Simplify:
5 . 5 . 5
5 . 5 . 5 . 5 . 5 . 5 . 5 . 5
=
1
5 . 5 . 5 . 5 . 5
=
1
55

4. The Rule:
•So when we had
37
33, we have seven 3’s in the numerator
and three 3’s in the numerator and three 3’s in the
denominator. Upon simplifying, there are more 3’s in the
numerator than the denominator. All 3 threes in the
denominator were cancelled out together with the 3
threes in the numerator. They equate to 1. There are now
4 threes left in the numerator that are not cancelled out,
which is the final answer.

5. The Rule:
When dividing two numbers having different exponents
but the same bases, we simply copy the base and subtract
the denominator’s exponent from the numerator’s
exponent. the exponents.
37
33 = 37 − 3
= 34
xm
xn
= xm −𝑛