Index (indices) in Maths is the exponent which is raised to a number. For example, in number 42, 2 is the index or power of 4. The plural form of index is indices. Also, a number of the form xn where x is a real number, x is multiplied by itself n times i.e. xn = x*x*x*x*x*——(n times). The number x is called the base and the super script n is called the index or power or exponent. In this article, you will learn the laws of the indices along with formulas and solved examples.
8 Laws of Indices
Any base variable raise to zero (0) is one (1) i.e. A0 = 1. For example, 20 = 1
If a base variable is raised to a negative number, then it will be equal to inverse of the base variable raised to a positive number i.e.
A-m = 1/Am
If a base number (which is a fraction) is raised to a number (m), then it will be equal to the numerator raised to the number (m) and the denominator raised to the same number (m) i.e.
(A/B)m = Am/Bm
Example, (2/3)2 = 22/32 = 4/9
If a base number is raised to a number (m) and multiply a base number of the same value raised to a number (n), then it will be equal to the base number raised to the sum of the exponents (m + n) i.e.
Am X An = Am+n
Example, y5 x y4 = y5+4 = y9
If a base number is raised to a number (m) and is divided by a base number of the same value raised to a number (n), then it will be equal to the base number raised to the difference between the exponents (m – n) i.e.
Am -:- An = Am-n
Example, 54 -:- 52 = 54-2 = 52 = 5 x 5 = 25
If a base variable is raised to a number (which is a fraction (x/y)), then it will be equal to the yth root of the base number raised to x i.e.
Ax/y = y√Ax
Example, 272/3 = 3√272 = 32 = 9
If a base varaible is raised to a number (n) and the entire number raised to power (m), then it is equal to the base number raised to the multiplication of the two exponents (m*n) i.e.
(Am)n = Amn
Example, (33)2 = 33*2 = 36 = 3*3*3*3*3*3 = 729
When two base variables with different bases, but same indices are multiplied together, we have to multiply the two bases and raise the same index to multiplied variables i.e.
An x Bn = (A.B)n
Example, 32 x 22 = (3*2)2 = 62 = 36
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