Power vs Exponent: Difference and Comparison

Power and exponents are used in early algebra, around middle school. It is almost always easy to distinguish between the two.

But as time passes, many adults have trouble using them correctly, and justifiably so, because there is little need for math or algebra in most of their lives.

Some students have this issue because these two words are closely related and belong to the same branch of mathematics. They are used interchangeably, which in turn, creates more confusion.

Key Takeaways

1. Power is the product of multiplying a number by itself a certain number of times.
2. An exponent is a small number written above and to the right of a base number that indicates how many times the base is multiplied by itself.
3. Power is a result, while exponent is a way to express how many times the base number is multiplied.

Power vs Exponent

The difference between power and exponent is that power is an expression that represents the repeated multiplication of a number by a certain factor, and the factor to which that multiplication is repeated is known as the exponent.

When a number is multiplied by itself many times to represent a larger number more conveniently, it is known as power. In contrast, the number of times that number is multiplied by itself in that expression is known as the exponent.

Comparison Table

Parameter of Comparison	Power	Exponent
Definition	Power can be defined as the number of times a number is multiplied by itself.	Exponent refers to the number of times a number is used in a multiplication.
Reference	When a number is raised to a certain degree using an exponent, the number or expression of the number as a whole is known as the power.	Exponent is the number to which a number is raised to define its power as a whole expression.
Position	Power is the whole number, including the base and the exponent. It has no specific position in that context.	The exponent is always written as a superscript of the number to which the power is raised.
Parts	A power, as used to describe an expression of a large number, has two parts, the base and the exponent.	Exponent has one part, the superscript number.
Operation	When two powers have the same base, they are multiplied.	When the bases are the same in power, the exponents are added.

What is Power?

The word power in mathematics, especially algebra, is used to represent a large number, making it easy to understand and use in calculations. A large number is raised to power. The quantity by which it is raised is written as a superscript and is known as the exponent.

Power has two main components – a base and an exponent. A base is a small number written normally. Exponent is the number written as a superscript to the base. Mathematically, power can be defined as base multiplied by itself exponent times.

A number written as a power means that that base number is multiplied by itself as many times as the exponent. This way, it is easy to read and use the number in operations and long and complicated calculations.

For example, the number 100000 is 10×10×10×10×10 and can be written as 10⁵ and then will be read as 10 to the power 5.

What is Exponent?

Mathematically, exponent refers to the small number written as a superscript of the base number. The base and the exponent represent a larger number, broken down into this form for easier calculations.

An exponent is a smaller positive integer. It implies how many times the base number should be multiplied to reach the power. Exponent is used interchangeably with power but has a different meaning and context.

When exponents are used to express a number, the process is termed as being raised to a power. Exponents may seem small and unimportant in basic algebra calculations, but they play a major role in bigger scientific notations and calculations.

In scientific notations and calculations, they represent very large numbers and accurate quantities in an easily readable way and can be used in other important calculations. For example, the distance between the sun and the earth is 1.496×10¹¹ million k.

In the case of exponents, certain operations can be performed on them, depending on different situations. These are very helpful in a lot of calculations.

Main Differences Between Power and Exponent

1. When a large number is expressed in a way that is easy to read and use in calculations, it is called being raised to power. The factor by which the number is raised is known as the exponent.
2. Power has two parts, the base and the exponent. The base represents the number that has been raised, and the exponent represents to which the base has been raised. The exponent has no other part since it is a part of power itself.
3. When a number is expressed so that it is multiplied by itself several times, it is known as a power. How many times that number is to be multiplied by itself is known as the exponent.
4. In the case of power, the number is written in the form of base and exponent and the whole is called the power. They both have their functions and are equally important and of significance. In the case of an exponent, the number is written as a superscript to the base. It represents great value.
5. When the base is the same, the power is multiplied. In the case of exponents, a series of operations can be performed. Exponents have more significance in the case of scientific calculations with big numbers.

References

1. https://www.sciencedirect.com/science/article/pii/S0960148102000666
2. https://www.nature.com/articles/332721a0

Last Updated : 11 June, 2023