Difference Between Power and Exponent

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

But as time passes, many adults have trouble with using them correctly, and justifiably so, because there is not much need for math or algebra in most of their lives.

Some students have this issue too because these two words are very closely related and belong to the same branch of mathematics. They are often used interchangeably, which in turn just 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 in order to represent a larger number more conveniently, it is known as the power, while the number of times that number is multiplied with 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 so as 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.	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 just has one part, the superscript number.
Operation	When two powers have the same base, they are multiplied.	When the bases are same in a power, the exponents are added.

What is Power?

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

A 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 with 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 the number as well as use it 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 together represent a larger number, which has been broken down to this form for easier calculations.

An exponent is usually a smaller positive integer. It implies how many times the base number should be multiplied with itself to reach the power. Exponent is often used interchangeable with power, but it 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 like 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 are used to represent very large numbers and accurate quantities in a way that is easily readable 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, there are certain operations that 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 as being raised to a 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 in such a way that it is multiplied by itself a number of 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 case of power, the number is written in the form of base and exponent and the whole is called as the power. They both have their functions and are equally important and of significance. In the case of exponent, the number is written as a superscript to the base. It represents a great value.
5. When the base is the same the power is multiplied. In the case of exponents, there are a series of operations that can be performed. Exponents have more significance in case of scientific calculations with big numbers.

References

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