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Step-by-step explanation:
(i)
(81/16)-¾
= (3/2)⁴ × -¾
= (3/2)-³
= (2/3)³
= (2×2×2/3×3×3)
= 8/27
The multiplicative inverse of 8/27 is 27/8.
(ii)
{(-3/2)-⁴}½
= {(2/-3)⁴}½
= {(2×2×2×2/(-3)×(-3)×(-3)×(-3))}½
= {16/81)½
= (4/9)² × ½
= 4/9
The multiplicative inverse of 4/9 is 9/4.
(iii)
(5/7)-² × (5/7)⁴ + (5/7)³
= (5/7)-²+⁴ + (5/7)³
= (5/7)² + 5/7)³
= 25/49 + 125/343
= 175/343 + 125/343
= 300/343
The multiplicative inverse of 300/343 is 343/300.