Properties III For every non-zero rational number `a/b` we have (i) `a/b -: a/b = 1` (ii) `a/b -: (- a/b) = -1` (iii) `((-a)/b) -: a/b = -1`

Properties II For any rational number (a)/(b) we have (a)/(b)-:1=(a)/(b) and (a)/(b)-:(-1)=-(a)/(b)=(-a)/(b)

For a non zero rational numbers a ,\ (a^3)^(-2) is equal to a^6 (b) a^(-6) (c) a^(-9) (d) a^1

For any two non-zero rational numbers a and b ,\ a^4-:b^4 is equal to (a-:b)^1 (b) (a-:b)^0 (c) (a-:b)^4 (d) (a-:b)^8

Let * be a binary operation on the set Q of rational numbers as follows: (i) a*b=a-b (ii) a*b=a^2+b^2 (iii) a*b=a+a b (iv) a*b=(a-b)^2 (v) a*b=(a b)/4 (vi) a*b=a b^2 Find which of the binary operations are commutative and which are associative

If a and b are non-zero rational numbers and n is a natural number then (a^(n))/(b^(n))=((a)/(b))^(n)

Fifth law If ab are non-zero rational numbers and n is an integer then ((a)/(b))^(n)=(a^(n))/(b^(n))

Sixth law If ab are non-zero rational numbers and n is a positive integer then ((a)/(b))^(-n)=((b)/(a))^(n)

For any two non-zero vectors a and b, |a|b+|b|a and |a|b-|b|a are

If a and b are two distinct non-zero real numbers such that a -b =a/b=1/b-1/a, then :