[27/125]^3/2 x [9/25]^-3/2
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Answer:
√(27/125)
Step-by-step explanation:
[27/125]³/² × [9/25]^-3/2
=> [ 3³/5³] ³/² × [ 3²/5²] ^-3/2
=> [3/5] ³*³/² × [ 3/5]^(2×(-3/2))
=> [3/5]⁹/² × [3/5]^-6/2
=> [ 3/5]^9/2 × [5/3]^6/2
=> (3⁹/² ÷ 3⁶/² ) × (5⁶/² ÷ 5⁹/²)
=> 3^(9/2-6/2) × 5^(6/2-9/2)
=> 3^(3/2) × 5^(-3/2)
=> 3^(3/2) ÷ 5^(3/2)
=> (3/5)³/²
(3/5)³/²=> √(27/125)
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