Question

What is laws of indices

Answer 1

To manipulate expressions, we can consider using the Law of Indices. These laws only apply to expressions with the same base, for example, 34 and 32 can be manipulated using the Law of Indices, but we cannot use the Law of Indices to manipulate the expressions 35 and 57 as their base differs (their bases are 3 and 5, respectively).

Answer 2

Properties of indices
b^m x b^n = b^(m+n)           (product law)
b^m/b^n = b^(m-n)               (quotient law)
(a^m)^n = a^m.n                  (Power law)
a^n/b^n=(a/b)^n                   ( Power of a product)
(a/b)^-n=(b/a)^n                    (Power of a quotient)
Special types
Negative index: If a≠0, then a^-m=1/a^m
Fractional index: a^1/3 = ∛a where 3=n; where n∈N