+3 votes
by kratos

Simplify:

(i) ((1/3)-3 – (1/2)-3) ÷ (1/4)-3

(ii) (32 – 22) × (2/3)-3

(iii) ((1/2)-1 × (-4)-1)-1

(iv) (((-1/4)2)-2)-1

1 Answer

+6 votes
by kratos
 
Best answer

(i) ((1/3)-3 – (1/2)-3) ÷ (1/4)-3

= (33 – 23) ÷ 43 (1/an = a-n)

= (27-8) ÷ 64

= 19 ÷ 64

= 19 × 1/64 (1/a ÷ 1/b = 1/a × b/1)

= 19/64

(ii) (32 – 22) × (2/3)-3

= (9 – 4) × (3/2)3 (1/an = a-n)

= 5 × (27/8)

= 135/8

(iii) ((1/2)-1 × (-4)-1)-1

= (21 × (1/-4))-1 (1/an = a-n)

= (1/-2)-1 (1/an = a-n)

= -21

= -2

(iv) (((-1/4)2)-2)-1

= ((-1/16)-2)-1 (1/an = a-n)

= ((-16)2)-1 (1/an = a-n)

= (256)-1 (1/an = a-n)

= 1/256

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