What is the value of (2/5)−1/2 × (5/2)1/2?

Concept: For a fraction raised to a negative exponent, invert the fraction and make the exponent positive: (a/b)−n = (b/a)n. And when two powers share the same base, multiplying them adds their exponents: am × an = am + n.

1. Rewrite the first factor using the negative-exponent rule: (2/5)−1/2 = (5/2)1/2.

2. The expression becomes (5/2)1/2 × (5/2)1/2 — a product of two powers with the same base, 5/2.

3. Add the exponents (they are equal, so the same-base rule applies directly): (5/2)1/2 × (5/2)1/2 = (5/2)1/2 + 1/2 = (5/2)1.

4. Simplify: (5/2)1 = 5/2.

Cross-check: (2/5)−1/2 = √(5/2) ≈ 1.58, and (5/2)1/2 = √(5/2) ≈ 1.58 as well; their product ≈ 2.5, matching 5/2 exactly.