When evaluating algebraic expressions,
1) you can add together like terms. $3x^5 + 6x^5 = 9x^5$, but you cannot add together different terms: $2x^4 + 3x^5$, because these have different exponents.
2) you can multiple different terms: $2x^4 \cdot 3x^5 = 6x^9$. When you multiple terms, the exponents are added together.
Why can't you add terms with different exponents?
Someone said it's because of the properties of algebra:
Commutative property: $a + b = b + a$ and $ab = ba$.
Associative property: $a + (b + c) = b + (c + a)$ and $a \cdot (b \cdot c) = b \cdot (a \cdot c)$.
Distributive property: $x(a+b) = xa + xb$.
So how do these properties suggest that you cannot add terms when exponents are different, but you can multiply terms with different exponents?