The rules are
[tex]x^a\cdot x^b = x^{a+b}[/tex]
[tex]\dfrac{x^a}{x^b} = x^{a-b}[/tex]
Let me show you why with a couple of examples: suppose we want to multiply
[tex]4^3\cdot 4^2[/tex]
Since powers are just repeated multiplications, we have
[tex]4^3\cdot 4^2 = \underbrace{4\cdot 4\cdot 4}_{4^3}\cdot\underbrace{4\cdot 4}_{4^2}=4^5 = 4^{3+2}[/tex]
Similarly, we have
[tex]\dfrac{4^3}{4^2} = \dfrac{4\cdot 4 \cdot 4}{4\cdot 4} = 4 = 4^1 = 4^{3-2}[/tex]
