What is Exponent?

An exponent of a number, represents the number of times the number is multiplied to itself. If 8 is multiplied by itself for n times, then, it is represented as:

8 x 8 x 8 x 8 x …..n times = 8ⁿ

The above expression, 8ⁿ, is said as 8 raised to the power n. Therefore, exponents are also called power or sometimes indices.

Examples:

• 2 x 2 x 2 x 2 = 2⁴
• 5 x 5 x 5 = 5³
• 10 x 10 x 10 x 10 x 10 x 10 = 10⁶

General Form of Exponents

The exponent is a simple but powerful tool. It tells us how many times a number should be multiplied by itself to get the desired result. Thus any number ‘a’ raised to power ‘n’ can be expressed as:

Here a is any number and n is a natural number.

aⁿ is also called the nth power of a.

‘a’ is the base and ‘n’ is the exponent or index or power.

 ‘a’ is multiplied ‘n’ times, and thereby exponentiation is the shorthand method of repeated multiplication.

Laws of Exponents

The laws of exponents are demonstrated based on the powers they carry.

• Bases – multiplying the like ones – add the exponents and keep the base same. (Multiplication Law)
• Bases – raise it with power to another – multiply the exponents and keep the base same.
• Bases – dividing the like ones – ‘Numerator Exponent – Denominator Exponent’ and keep the base same. (Division Law)

Let ‘a’ is any number or integer (positive or negative) and ‘m’,  ‘n’ are positive integers, denoting the power to the bases, then;