Simplify the Exponential Product: 3^x ⋅ 2^x ⋅ 3^(2x)

Because exponent rules only work with identical bases! Think of it this way: $3^2 \cdot 2^2 = 9 \cdot 4 = 36$, but $5^2 = 25$ and $6^2 = 36$. Only 6^2 gives the right answer by coincidence at this specific value.

Only combine terms with exactly the same base. In $3^x \cdot 3^{2x}$, both have base 3, so you can add exponents: $x + 2x = 3x$. Keep $2^x$ separate because it has a different base.

These are completely different! $3^{3x}$ means the exponent is 3x, while $(3^3)^x = 27^x$ means 27 raised to the x power. Parentheses matter in exponents!

No! The distributive property doesn't work with exponents. $3^{x+2x} = 3^{3x}$, not $3^x + 3^{2x}$. When multiplying powers with the same base, add the exponents.

Substitute a simple value like x = 1. Original: $3^1 \cdot 2^1 \cdot 3^2 = 3 \cdot 2 \cdot 9 = 54$. Your answer: $3^3 \cdot 2^1 = 27 \cdot 2 = 54 ✓$

Keep each different base separate! For example, $2^x \cdot 3^{2x} \cdot 5^x$ stays as is because all bases are different. You can't combine any of these terms.