Simplify: (81³⁄⁴ × (1/27)⁻²⁄³) / ((√32 + √8)² − (√32 − √8)²)
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Correct answer: A
Explanation
Given:
(81³⁄⁴ × (1/27)⁻²⁄³) / ((√32 + √8)² − (√32 − √8)²)
By the formula:
(a + b)² − (a − b)² = 4ab
81³⁄⁴ = (3⁴)³⁄⁴ = 3³ = 27
(1/27)⁻²⁄³ = 27²⁄³ = (3³)²⁄³ = 3² = 9
Upper part = 27 × 9 = 243
(√32 + √8)² − (√32 − √8)²
= 4 × √32 × √8
= 4 × √256
= 4 × 16
= 64
Value = 243 / 64