What are exponents and powers ?

Exponents and Power.

Very large numbers are difficult to read, understand, compare and operate upon. To make all these easier, Exponent or power is used to convert many of the large numbers into a shorter form.

Exponent -The short notation $a^m$ stands for the product $a\times a\times a...m\mathrm{times}$. Here $‘a’$ is called the base and ‘$‘m’$’ is called the exponent. Power-The same short notation $a^m$ is read as $‘a’$ raised to the power of $‘m’$ or simply as the $m\mathrm{th}$ power of $‘a’$.

$a^m$ is called the exponential form of the product $a\times a\times a...m\mathrm{times}$.

Examples:

$$\begin{gathered} \left(i\right){10}^4=10\times 10\times 10\times 10=10000 \\ \left(ii\right){10}^{-4}=\frac{1}{10\times 10\times 10\times 10}=0.0001 \\ \left(iii\right)3.45\times {10}^4=3.45\times 10\times 10\times 10\times 10=34500 \end{gathered}$$

Therefore, exponents and powers are being used to express extremely big as well as extremely tiny values by the notation $a^m$