Simplify the following : (i) (-1/27)-2/3

(i) (-1/27)^-2/3

Solution:

(-1/27)^-2/3

= (-1/3³)^-2/3

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

= (-1/3)^-2

= (-3)²

= 9

(ii) (64)^-2/3 ÷ 9^-3/2

Solution:

(64)^-2/3 ÷ 9^-3/2

We can write it as

= (4³)^-2/3 ÷ (3²)^-3/2

By further calculation

= 4 ^{3 ×- 2/3} ÷ 3 ^{2 × -3/2}

So we get

= 4^-2 ÷ 3^-3

= 4^-2/ 3^-3

It can be written as

= 1/4² / 1/3³

= 3³/4²

We get

= 27/16

= 1 11/16

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