A term that represents a quantity as a product of two or more exponential terms simply is called a simple exponential term.

Some quantities cannot be written in exponential notation purely due to involvement of other number or numbers. So, the quantity is simply expressed as the product of two or more exponential terms. The product of them is also a term basically. Hence, the term is called a simple exponential term.

$1701$ $\,=\,$ $7 \times 3 \times 3 \times 3 \times 3 \times 3$

$\implies 1701$ $\,=\,$ $7 \times 3^5$

$\,\,\, \therefore \,\,\,\,\,\, 1701$ $\,=\,$ $7(3^5)$

The quantity $1701$ is written as $7(3^5)$ simply in exponential form and it cannot be expressed as a pure exponential term due to the involvement of unlike factors $3$ and $7$. Therefore, the term $7(3^5)$ is called a simple exponential term.

$11250$ $\,=\,$ $2 \times 3 \times 3 \times 5 \times 5 \times 5 \times 5$

$\implies 11250$ $\,=\,$ $2 \times 3^2 \times 5^5$

$\,\,\, \therefore \,\,\,\,\,\, 11250$ $\,=\,$ $2(3^2)(5^4)$

The term $2(3^2)(5^4)$ is called a simple exponential term.

The following are the best examples for simple exponential terms.

$(1) \,\,\,\,\,\,$ $-7(4^{-6})(5^8)$

$(2) \,\,\,\,\,\,$ $ 3^4 (5^7)(7^9)(11^{11})$

$(3) \,\,\,\,\,\,$ $1.23^8$

$(4) \,\,\,\,\,\,$ $\dfrac{1}{4}{\Bigg(\dfrac{3}{5}\Bigg)}^2$

$(5) \,\,\,\,\,\,$ $6{(17)}^{\frac{2}{5}}$

Observe the third example. The exponential term $1.23^8$ is a pure exponential term but it can be written as $1 \times (1.23^8)$ or $4^0 \times (1.23^8)$ and etc. because any number raised to the power of zero is equal to one as per zero exponent rule. Therefore, a pure exponential term is also a simple exponential term but a simple exponential term is not always a pure exponential term.

Latest Math Topics

Apr 18, 2022

Apr 14, 2022

Apr 05, 2022

Mar 18, 2022

Mar 05, 2022

Latest Math Problems

Apr 06, 2022

Mar 22, 2022

A best free mathematics education website for students, teachers and researchers.

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

Learn how to solve the maths problems in different methods with understandable steps.

Copyright © 2012 - 2021 Math Doubts, All Rights Reserved