Simplify (2x³y²)³ ÷ (4x⁵y), then solve 3^(2x−1) = 27.

1. 1 · Apply the power law to the bracket. (2x³y²)³ = 8x⁹y⁶.
2. 2 · Divide using the quotient law. 8x⁹y⁶ ÷ 4x⁵y = 2x⁴y⁵.
3. 3 · Write both sides of the equation with the same base. 27 = 3³, so 3^(2x−1) = 3³.
4. 4 · Equate the indices and solve. 2x − 1 = 3, so 2x = 4 and x = 2.
5. 5 · Check. 3^(2×2−1) = 3³ = 27. ✓

Scoring tip: Name each law as you use it; the method marks come from those lines.