Second law If a is a non - zero rational number and `m n` are integers then `a^m -: a^n = a^(m-n) or a^m/a^n = a^(m-n)`

First law If a is a non-zero rational number and mn are integers then a^(m)a^(n)=a^(m+n)

Third law If a is a non-zero rational number and mn are integers then (a^(m))^(n)=a^(mn)=(a^(n))^(m)

First law if is any non -zero rational number andmn are natural numbers then a^(m)xx a^(n)=a^(m)+n

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

Second law if a any non -zero rational number and m and n are natural numbers such that m>n then a^(m)-:a^(n)=a^(m)-n or (a^(m))/(a^(n))=a^(m)-n

Generalisation : if a is a non - zero rational number and mnp are natural numbers then a^(m)xx a^(n)xx a^(p)=a^(m)+n+p

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)

If x be any non zero integer and m, n be negative integers. Then x^(m)xxx^(n) is equal to

Third luw if a is any rational number different from zero and mn are natural numbers then (a^(m))^(n)=a^(m)-n=(a^(n))^(m)