# Exponential Terms

Exponential Terms

In the below image, there are several butterflies of the same species. Now can you think of a way to write many numbers in a simplified form? In maths, we use exponents to express many numbers in a single expression.

The number 2 multiplied 7 times to itself, can be expressed as:  $2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 2^7$

In this mini-lesson, we will learn more about exponents and how we can use them in math.

## Lesson Plan

 1 What Do You Understand by Exponential Terms? 2 Tips and Tricks 3 Important Notes on Exponential Terms 4 Solved Examples on Exponential Terms 5 Interactive Questions on Exponential Terms

## What do you Understand by Exponential Terms?

The variables having powers or index are called exponential terms.

The standard form of an exponent is $$a^n$$.

$a^n = a \times a \times a \times .... n~times$

Here 'a' is the base and 'n' is called the power, exponent, or index.

And it is read as 'a to the power of n'.

n can have values of whole numbers, integers, fractions, or decimals.

Some of the examples of exponential terms are :

$$2^5, (-4)^{0.2}, 5^{\frac{2}{3}}$$

Further, the following formulae are used to simplify exponents.

• $$a^m \times a^n = a^{m + n}$$
• $$\dfrac{a^m}{ a^n} = a^{m - n}$$
• $$(a^m)^n= a^{m \times n}$$
• $$a^{-m} = \dfrac{1}{a^m}$$
• $$\sqrt [n] a^m= (a^m)^{\frac{1}{n}} =a^{\frac{m}{n}}$$ Tips and Tricks
1. The number 1 raised to any power is 1 itself. $1^n = 1$
2. Any number raised to the power of 0 is 1. $n^0 = 1$
3. A fraction can be written as an exponent raised to the power of -1. $\dfrac{1}{n} = n^{-1}$

## How to simplify Exponential Terms raised to an exponent?

Exponential terms raised to an exponent can be conveniently transformed into simplified form.
$(a^m)^n = a^{m \times n}$

### Examples:

A few examples listed below would help us to understand the simplification of exponential terms.

• $$(2^4)^3 = 2^{4 \times 3} = 2^{12}$$
• $$(((5^2)^2)^2)^2 = 5^{2 \times 2 \times 2 \times 2} = 5^{16}$$
• $$(3^4)^5 = 3^{4 \times 5 } = 3^{20}$$
Exponents and Logarithms
Grade 9 | Questions Set 1
Exponents and Logarithms
Exponents and Logarithms
Grade 9 | Questions Set 2
Exponents and Logarithms
More Important Topics
Numbers
Algebra
Geometry
Measurement
Money
Data
Trigonometry
Calculus
More Important Topics
Numbers
Algebra
Geometry
Measurement
Money
Data
Trigonometry
Calculus