Simplify: 3⁴ ÷ 3².

**The reasoning** This tests the **Law of Indices for Division**: when dividing powers with the same base, you *subtract* the exponents. So: 3⁴ ÷ 3² = 3⁴⁻² = 3² = **9** Think of it this way: 3⁴ means 3 × 3 × 3 × 3 = 81, and 3² means 3 × 3 = 9. When you divide: 81 ÷ 9 = 9. The shortcut is just subtract the powers! **Why the wrong options tempt you** - **A) 3** — You might subtract 4 − 2 = 2 but forget to calculate 3². Don't stop halfway! - **B) 6** — This tricks students who *add* instead of subtract (3⁴⁺² would be wrong anyway), or who mistakenly do 3 × 2. - **D) 27** — You might add the exponents (4 + 2 = 6, then... confusion), or calculate 3³ instead of 3². **Quick takeaway** "Same base division? Subtract the powers, then evaluate." Write it down: aⁿ ÷ aᵐ = aⁿ⁻ᵐ — this formula is your best friend in indices questions! 💪