Students often encounter confusion when learning exponent multiplication rules. Understanding common misconceptions helps build a solid foundation:
Misconception 1: Multiplying the Exponents
Incorrect: a³ × a² = a⁶ (multiplying exponents)
Correct: a³ × a² = a⁵ (adding exponents)
When multiplying powers with the same base, we add the exponents, not multiply them.
Misconception 2: Different Bases
Incorrect: 2³ × 3² = 6⁵ (combining different bases)
Correct: 2³ × 3² = 8 × 9 = 72 (calculate separately)
The multiplication rule only applies when the bases are identical.
Misconception 3: Confusing with Power of Power Rule
Multiplication Rule: a^m × a^n = a^(m+n)
Power of Power Rule: (a^m)^n = a^(m×n)
These are different operations with different rules.