The document provides instructions for dividing terms with algebraic exponents. It explains that to divide algebraic exponent terms, one should write the division as a fraction and separate the numbers from the variables with exponents. Then, reduce the numerical fraction and use the exponent subtraction rule, which states that if the bases are the same, subtract the exponents. This allows one to simplify the algebraic exponent terms in the division. Several examples are shown applying these steps to divide various algebraic exponent terms.

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2. 23
22
Rewrite as a Fraction
= 23
Fully Expand the Powers out
22
= 2 x 2 x 2 and then cancel all identical
2 x 2 items in the top and bottom
= 2

3. Let’s consider am
an
or am
an
If we have any base that is the same “a”,
then we can skip expanding and cancelling
the exponents “m’ and “n”, and use the fast
track rule and SUBTRACT the Exponents
am
an
= am - n
This rule works for both letters and numbers

4. 23
22
Rewrite as a Fraction
= 23
Use the Subtract Powers shortcut Rule
22
= 2 3 – 2
If Bases are the same, then subtract the
Powers, which is the Exponents Divide Rule.
= 21
= 2

5. k5
k3
Rewrite as a Fraction
= k5
Use the Subtract Powers shortcut Rule
k3
= k 5 – 3
If Bases are the same, then subtract the
Powers, which is the Exponents Divide Rule.
= k2

6. To Divide Algebra Exponents Terms, follow these steps:
 Write any question as a big Fraction
 Separate out Numbers and Algebra Exponents
 Reduce down the Numbers Fraction
 Apply the Exponents Subtraction Rule to same Bases
 Write Final Answer as a Fraction without x signs

7. 12w3
6w2
Rewrite as a Fraction
= 12w3
Separate Numbers and Letters
6w2
= 12 x w3
Reduce down number Fraction
6 x w2
and use Powers Subtract Rule
= 2 x w3 - 2
= 2w1
= 2w
2

8. 12a7
b5
16a2
b2
Rewrite as a Fraction
= 12a7
b5
Separate Numbers & Letters
16a2
b2
= 12 x a7
x b5
Reduce down number Fraction
16 x a2
x b2
and use Powers Subtract Rule
= 3 x a7 - 2
x b5 - 2
= 3 x a5
x b3
= 3a5
b3
4 4 4
3
4

9. -e2
h - 8eh Rewrite as a Fraction
= -e2
h Write Numbers as Factors
-8eh and Expand all Variables
= - 1 x e2
x h Fill empty tops with 1’s
- 8 x e1
x h Apply Subtract Rule
= 1 x e2 - 1
x 1 = 1e = e
8 8 8

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