Table of Content

• What is an Exponent?
• Important Laws Related to Exponents
• What is Power?
• Important Rules Related to the Power
• Difference Between Exponent and Power
• Properties of Exponents
• Properties of Powers
• Applications of Exponents and Powers

Characteristic	Exponent	Power
Definition	The multiplicity of a base by itself is represented by this number.	a base raised to an exponent’s result.
Notation	Appears as a superscript to the right of the base (e.g., in 23, 3 is the exponent).	Refers to the entire expression (e.g., in 23 = 8, 8 is the power).
Role	shows how often the base is applied as a factor.	describes the operation’s result.
Components	A portion of the statement designates the base operation to be carried out.	the value that results from carrying out the operation that the exponent indicates.
Example	In 72 = 81, 2 is the exponent.	In 72 = 49, 49 is the power.
Context of Use	used to define the calculation process required to determine the power.	used to express how exponentiation produces a numerical result.
Formula Representation	The portion of the base-exponent notation that shows how frequently the base is a factor.	the whole expression, which yields a particular value and includes the base and the exponent.

Properties of Exponents

Exponents are governed by certain principles that make math operations easier. To effectively solve challenging mathematical problems, these qualities are necessary.

Product of Powers:

a^m × aⁿ = a^{m + n}

Quotient of Powers:

a^m/aⁿ = a^{m – n}

Power of a Power:

(a^m)ⁿ = a^{m × n}

Power of a Product:

(ab)ⁿ = aⁿ × bⁿ

Zero Exponent:

a⁰ = 1 ( where a ≠ 0)

Negative Exponent:

a^-n = 1/aⁿ

Properties of Powers

The way powers respond under different operations is described by their attributes, which are derived from the properties of exponents.

Power of a Product:

(ab)ⁿ = aⁿ × bⁿ

Power of a Quotient:

(a/b)ⁿ = aⁿ / bⁿ

Power of a Power:

(a^m)ⁿ = a^{m × n}

Applications of Exponents and Powers

Exponents and powers are essential tools in mathematics and science since they may be applied in a multitude of domains.

Scientific Notation

In scientific notation, exponents are frequently employed to compactly express very big or very small quantities.

Example

5.97 × 10²⁴ ( the mass of Earth in kilograms)

Compound Interest

In finance, exponents are used to calculate compound interest.

Formula:

A = p(1 + r/n)^nt

Where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount.
• r is the annual interest rate (decimal).
• n is the number of times interest is compounded per year.
• t is the time the money is invested in years.
• Growth and Decay

Processes like microbiological growth, radioactive decay, and population increase are all described by exponential functions.

Computer Science

In computer science, exponents are used to analyze the difficulty of algorithms, especially those with logarithmic and exponential time complexities.

Physics and Engineering

Exponents are employed in physics and engineering to explain several phenomena, including signal attenuation, energy levels, and wave propagation.

Examples on Exponent and Power

Example 1: What is the value of 2⁴?

Solution:

= 2⁴

= 2 × 2 × 2 × 2 = 16

Example 2: What is 3⁰?

Solution:

3⁰ = 1

Example 3: Simplify: (2³)².

Solution:

(2³)² = 2^3×2

= 2⁶= 2 × 2 × 2 × 2 × 2 × 2

= 64

Example 4: What is 3.2×10³ in standard form?

Solution:

3.2 × 10³ = 3200

Example 5: What is the value of (-2)⁴?

Solution:

(-2)⁴ = -2 × -2 × -2 × -2

= 16

Practice Questions on Exponent and Power

Q1. Simplify 5² × 5³

Q2. What is 7⁰?

Q3. Simplify: 5⁴ / 5³.

Q4. What is 3^-2.

Q5. What is ( 2 × 5)³.

Answer Key

• Answer 1: 5⁵
• Answer 2: 1
• Answer 3: 5
• Answer 4: 1/9
• Answer 4: 1000

Conclusion

Comprehending the distinction between exponent and power is essential for grasping mathematical ideas and effectively resolving intricate issues. Power is the outcome of multiplying a base by itself; exponents show how many times a base is multiplied by itself.

Because of their ability to simplify mathematical processes, exponents and powers are useful tools in a variety of industries, including science, economics, and engineering. Students and professionals can improve their problem-solving abilities and successfully use mathematical concepts in practical settings by understanding these ideas.

Also Read:

• Practice Questions on Exponent and Power
• Exponent: Definition, Formula, Laws and Examples
• Real-Life Applications of Exponent and Power

Difference Between Exponent and Power – FAQs

Are Exponent and Power the Same Thing?

In simple terms, power can be defined as an expression that represents repeated multiplication of the same number whereas exponent is the quantity that represents the power to which the number is raised. Both these terms are often used interchangeably in mathematical operations.

What is the Difference between Exponent and Power?

The number that represents the number of times the base is multiplied by itself is called the exponent. The outcome of elevating the base to the exponent is referred to as power.

How do Exponents with the Same Base be Multiplied?

Exponents should be added in order to multiply them by the same base:

a^m × aⁿ = a^m+n

Describe the Rule of Zero Exponent.

According to the zero exponent rule, every non-zero base raised to the power of zero equals one:

a⁰ = 1