Simplify the following: (i) (81/16)-3/4.

Simplify the following:

(i) (81/16)^-3/4

Solution:

(81/16)^-3/4

= [(3⁴/2⁴)]^-3/4

= [(3/2)⁴]^-3/4

= (3/2)^{-3/4 x 4}

= (3/2)^-3

= (2/3)³

= 2³/3³

= (2 x 2 x 2)/(3 x 3 x 3)

= 8/27

(ii) 

Solution:

= (5/4)^{3 x -2/3}

= (5/4)^-2

= (4/5)²

= 16/25

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