Answer:
We have to match each exponents expressions with its rule.
Given the exponent expressions:
1.
[tex]A^m \cdot A^n[/tex]
⇒[tex]A^{m+n}[/tex]
2.
[tex](AB)^m[/tex]
⇒[tex]A^m \cdot B^m[/tex]
3.
[tex](A^m)^n[/tex]
⇒[tex]A^{mn}[/tex]
4.
[tex]a^0[/tex]
⇒[tex]1[/tex]
5.
[tex]A^{-n}[/tex]
⇒[tex]= \frac{1}{A^n}[/tex]
Therefore,
Matching of the given expression with its rule are as follow.
1. [tex]A^m \cdot A^n[/tex] → E
2. [tex](AB)^m[/tex] → A
3. [tex](A^m)(A^n)[/tex] → C
4. [tex]a^0[/tex] → B
5. [tex]A^{-n}[/tex] → D
