(Guidance Programme) Combined Graduate Level Exam - Tier - II : Indices and Surds

Indices and Surds

Indices

In the expression xn, n is called the exponent or index and x is called the base and xn is read as ‘x to the power of n’ or ‘x raised to the power n’.
eg,
1. 36 = 3 × 3 × 3 × 3 × 3 × 3 = 729
43 = 4 × 4 × 4 = 64
The expression (xm)n is read as ‘x raised to the power m whole raised to the power n’.
2. (24)3 = (16)3 = 212
The expression is read as ‘x raised to the power m power n’.
3. = 264
Hence, (xm)n¹

Laws of Indices

1. am × an = am + n

2. (am)n = amn

3. (ab)m = am bm

4. a0 = 1 if (a ¹ 0)

5. When the bases of two numbers are equal, then their powers are also equal. eg, If 3n = 32, then, n = 2.

6. When the powers of two numbers are equal, then their bases are equal. eg, If a3 = 43, then a = 4. Where a is a positive real number and n is a rational number.