(¾)⁷ × (4/3)⁷ = ?

Question

(¾)⁷ × (4/3)⁷ = ?

1. A. 1 (Correct answer)
2. B. 0
3. C. 14
4. D. -1

Correct Answer

Option A — 1

Detailed Solution & Explanation

The correct answer is 1.

Key Points

• (3/4)⁷ × (4/3)⁷ = [(3/4) × (4/3)]⁷ = 1⁷ = 1.
• Since the bases are reciprocals raised to the same power, the product is always 1.

Additional Information

• Law used: aⁿ × bⁿ = (ab)ⁿ. Also recall a⁰ = 1 for any a ≠ 0.
• The full set of exponent laws tested at this level:
  • aᵐ × aⁿ = aᵐ⁺ⁿ and aᵐ ÷ aⁿ = aᵐ⁻ⁿ
  • (aᵐ)ⁿ = aᵐⁿ
  • (a/b)ⁿ = aⁿ/bⁿ and (a/b)⁻ⁿ = (b/a)ⁿ
• Recognising the reciprocal pair saves all the arithmetic — never expand (3/4)⁷ by hand.