Pure Exponential Term

An exponential term which contains a base and a power purely, is called a pure exponential term.

Introduction

Some numbers can be expressed in exponential form on the basis of another number purely. If the term is purely in the form a base and a power, then the term is called a pure exponential term.

Example

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

In this example, the quantity $625$ is split as the multiplicative factors on the basis of another number $5$ and the number of multiplying factors is $4$. Hence, the number $625$ is written as $5^4$ in exponential notation.

Actually, $5^4$ represents the quantity $625$ in exponential form but it is a term basically but the term $5^4$ is written purely in terms of a base and a number. Therefore, the exponential term $5^4$ is called a pure exponential term mathematically.

Examples

Look at the following examples to understand the concept of pure exponential term.

$(1) \,\,\,\,\,\,$ $3^{-7}$

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

$(3) \,\,\,\,\,\,$ ${(0.52)}^6$

$(4) \,\,\,\,\,\,$ ${\Bigg(\dfrac{3}{5}\Bigg)}^2$

$(5) \,\,\,\,\,\,$ ${(8)}^{\frac{3}{4}}$