Indices

Indices

Indices, (also known as exponents or powers), are a way of representing how many times a number or variable (the base) is multiplied by itself. For example, in \(2^3\), 2 is the base, and 3 is the index (or exponent), meaning \(2 \times 2 \times 2 = 8\).

\(\text{So, } a \times a \times a \times a = a^4\)

Formula for Indices

Here are some key formulas for working with indices:

1. Multiplication Rule: \( a^m \times a^n = a^{m+n} \)

2. Division Rule: \( \frac{a^m}{a^n} = a^{m-n} \) (where \( a \neq 0 \))

3. Power of a Power Rule: \( (a^m)^n = a^{m \times n} \)

4. Power of a Product Rule: \( (ab)^n = a^n \times b^n \)

5. Zero Exponent Rule: \( a^0 = 1 \) (where \( a \neq 0 \))

6. Negative Exponent Rule: \( a^{-n} = \frac{1}{a^n} \)

7. \(n^th\) Root Rule: \( \sqrt[n]{a} = a^{\frac{1}{n}} \)

Example Questions with solutions