Simplify the following: (i) (8/125)-1/3

(i) (8/125)^-1/3

Solution:

(8/125)^-1/3

= [(2 x 2 x 2)/(5 x 5 x 5)]^-1/3

= (2³/5³)^-1/3

= (2/5)^{3 x -1/3}

= (2/5)^-1

= 5/2 = 2½

(ii) (0.027)^-1/3

Solution:

(0.027)^-1/3

= (27/1000)^-1/3

= [(3 x 3 x 3)/(10 x 10 x 10)]^-1/3

= (3³/10³)^-1/3

= (3/10)^{3 x -1/3}

= (3/10)^-1

= 10/3

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