The Laws of the Indices

The Laws of the Indices

Laws of Indices

Basic Laws

• An index tells us how many times a number is multiplied by itself.
• Any number raised to the power of zero is equal to 1. For instance, 8^0 = 1.
• Any number raised to the power of one is the number itself. For instance, 6^1 = 6.

Multiplication and Division

• When multiplying terms with the same base, add the indices. For instance, a^m x a^n = a^(m+n).
• When dividing terms with the same base, subtract the indices. For instance, a^m / a^n = a^(m-n).

Power of a Power Rule

• When a term with an index is raised to another power, multiply the indices. For instance, (a^m)^n = a^(mn).

Negative Indices

• A term with a negative index is equal to one divided by the same term with a positive index. So, a^-n = 1/ a^n.

Fractional Indices

• A term with a fractional index involves both roots and powers. For instance, a^(1/n) is the n-th root of a, and a^(m/n) is the n-th root of a, raised to the power m.
• It’s important to remember that a square root could also be written as a^(1/2), a cube root as a^(1/3), and so on.