Law of Exponents

If a is a rational number, multiplied by itself m times, it is written as am. a is called the base and m is called the exponent.

Exponential Notation

Consider the following products:

  • (i) 7 × 7
  • (ii) 3 × 3 × 3
  • (iii) 6 × 6 × 6 × 6 × 6

In (i), 7 is multiplied twice and hence 7 × 7 is written as 72.

In (ii), 3 is multiplied three times and so 3 × 3 × 3 is written as 33.

In (iii), 6 is multiplied five times, so 6 × 6 × 6 × 6 × 6 is written as 65.

72 is read as 7 raised to the power 2 or second power of 7. Here, 7 is called base and 2 is called exponent (or index).

Similarly, 33 is read as 3 raised to the power 3 or third power of 3. Here, 3 is called the base and 3 is called exponent.

Similarly, 65 is read as 6 raised to the power 5 or fifth power of 6. Again 6 is base and 5 is the exponent (or index).

If a is a rational number, multiplied by itself m times, it is written as am. a is called the base and m is called the exponent.

Laws of Exponents