(i) (1/4)-4 × (1/4)-8 = (1/4)-4x
(1/4)-4-8 = (1/4)-4x (an × am = an+m)
(1/4)-12 = (1/4)-4x
When the bases are same we can directly equate the coefficients.
-12 = -4x
x = -12/-4
= 3
(ii) (-1/2)-19 ÷ (-1/2)8 = (-1/2)-2x+1
(1/2)-19-8 = (1/2)-2x+1(an ÷ am = an-m)
(1/2)-27 = (1/2)-2x+1
When the bases are same we can directly equate the coefficients
-27 = -2x+1
-2x = -27-1
x = -28/-2
= 14
(iii) (3/2)-3 × (3/2)5 = (3/2)2x+1
(3/2)-3+5 = (3/2)2x+1 (an × am = an+m)
(3/2)2 = (3/2)2x+1
When the bases are same we can directly equate the coefficients
2 = 2x+1
2x = 2-1
x = 1/2
