# Exponential term

## Definition

A term that expressed in exponential notation to represent a quantity is called an exponential term.

Any number can be written in exponential form on the basis of another number to represent the quantity simply and that term is called an exponential term.

For example, $64$ is a number and it can be written in exponential form on the basis of number $2$.

$64 \,=\, 2 \times 2 \times 2 \times 2 \times 2 \times 2 \,=\, 2^6$

The number $64$ is written in exponential form as $2^6$ and therefore, the term $2^6$ is called an exponential term.

### Types of terms

Exponential terms are usually appeared in two forms.

01

#### Pure Exponential term

This type of exponential term is purely in exponential form. For example, $625$ is a number and express it in exponential notation.

$625 = 5 \times 5 \times 5 \times 5 = 5^4$

The number $625$ is purely expressed in exponential form as $5^4$. Hence, the exponential term $5^4$ can be called as a pure exponential term.

The following examples are best examples for this type of exponential terms.

$3^{-7}$, $\,\, {(-5)}^4$, $\,\, {(0.52)}^6$, $\,\, {\Bigg(\dfrac{3}{5}\Bigg)}^2$, $\,\, {(8)}^{\frac{3}{4}}$

02

#### Simple exponential term

For example, $405$ is a number and factorize the number to express it in exponential notation.

$405 \,=\, 5 \times 3 \times 3 \times 3 \times 3$
$\implies 405 \,=\, 5 \times 3^4$
$\implies 405 \,=\, 5(3^4)$

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