Base and Exponents

The concept of “Base and Exponent” is mainly introduced to make reading and writing a huge numbers easier.

For example $10^{6}=1000000$

Definition

Base and exponents

The base of an exponent is a number that is raised to a certain power. So, the base of an exponent represents the number that is multiplied by itself.

The exponent represents how many times the base number is multiplied.

The power can be defined as the number obtained by raising the base number to the exponent. So, it refers to the complete expression.

In the figure, $2$ is the base , $3$ is an exponent. $8$ is the power.

Here $2^{3}$ is read in many ways

• $2$ to the power of $3$
• $2$ raised to $3$

Negative Bases

Case 1: If the base is negative and the exponent is an even number, the power is positive.

$(-5)^{2}=-5\times -5=25$

Case 2: If the base is negative and the exponent is an odd number, the power is negative.

$(-5)^{3}=-5\times -5\times -5=125$

Also $(-a)^{n}\neq -a^{n}$

$(-5)^{2}\neq -5^{2}$

$25\neq -25$