# Exponents - Only Natural Numbers

A power is an abbreviated form of writing a multiplication formed by several equal factors.

6 x 6 x 6 x 6 x 6 x6 x 6 = 67

## Exponent

The exponent of a power indicates the number of times to multiply the base by itself, in the above case, 7.

## Properties of the Powers of Natural Numbers

1) a0= 1

2) a1= a

3) Product of powers with the same base:

Then the exponent is the sum of the exponents.

am x a = am + n

Demonstration :

8x 8= 85 + 2 = 87

4) Division of powers with the same base:

Then exponent is the difference between the exponents.

ax a = am − n

Demonstration :

2: 2= 25 − 2 = 23

5) Power of a power:

Then the exponent is the product of the exponents.

(am)n = am x n

Demonstration :

(85)3 = 815

6) Multiplication of powers with the same exponent:

Then base is the product of the bases.

ax b = (a x b) n

Demonstration :

2x 6= 123

7) Division of powers with the same exponent:

Then base is the quotient of the bases.

a/ b= (a / b)n

Demonstration :

12/ 4= 33