Question

Prove that (81/16)^-3/4 ×[(25/9)^-3/2 ÷ (5/2)^-3]=1​

Answer 1

Answer:

First write them in positive exponent form

(16/81)¾ × [ (9/25)^3/2 ÷ (2/5)³ ]

(2⁴×¾)/ (3⁴×¾) × [ (3² × ^3/2) / (5² ×^3/2) ÷ 2³/5³)

Simplify the terms

2³/3³ × ( 3³ / 5³ ÷ 2³/5³)

Solve the terms in the bracket

2³/3³ × (3³/5³×5³/2³)

You will get

2³/3³ × 3³/2³ = 1

They will cancel each other so the answer will be 1

Hope this helps.