Difference Between Power And Exponent: Definition and Explanation

Many students find it hard to pinpoint the difference between power and exponent as these words are very closely related and belong to the same branch of mathematics. The term power is used to indicate the number of times a certain integer is multiplied by itself. The Term exponent however indicates the number of times the number is used in the whole setting. For instance, 52 is the power where 5 is the base and 2 is the exponent. 

In mathematics, superscript is the little digit placed above and to the right of any number. Since, large numbers are difficult to read, compare and operate due to which they are denoted in the form of small numbers with the help of superscripts, and this is done with the help of powers and exponents. To put it simply, Power is a term that depicts repeated multiplication of the same number, whereas exponent is the amount that reflects the number increasing power. In mathematical operations, both of these phrases are frequently used interchangeably. Let us discuss how power can be differentiated from the exponent in detail. 

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What is Power?

In mathematics, the term "power" refers to the repeated multiplication of the same integer. The power of a number specifies how many times that number should be multiplied. In mathematical terms, if someone writes 24, it means that “2 is raised to the power 4” or “ two is multiplied by itself 4 times”. In this scenario, the whole context 2 will be the base, and 4 is the exponent. 

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Some of the special terms that are used in the case of powers are:

When a number is:

• Squared – power is 2
• cubed – Power is 3
• “to the power of” – used for powers more than 3

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What is Exponent?

Exponent is generally defined as a positive or negative number that represents the power to which the base number is to be raised. An exponent is commonly displayed as a raised symbol next to the number or phrase. For example, 24, 4 is the exponent. It signifies how many times the base number is multiplied by itself. An exponent can either be constants, numbers, or any variables. Moreover, exponents represent the times the base number has to be multiplied. Usually, the large numbers are expressed using exponents. This process is called the raising to a power. Also, there are some important rules while performing some arithmetic operations with exponents. They are:

• x⁰ = 1
• (x^m)ⁿ = x^mn
• x^m × y^m = (xy)^m
• x^m ÷ y^m = (x/y)^m
• x^m × xⁿ = x^m+n
• x^m ÷ xⁿ = x^m-n

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Difference between Power and Exponent

The major differences between power and exponent are as follows:

Let us take an example to understand the difference between power and exponent,

“ 4 x 4 x 4 x4 x 4 = 10²⁴ “

This can be written as 45 = 10²⁴

Here, It simply means that the number ‘4’ is multiplied five times by itself to get the number 10²⁴. It can be said that “4 raised to power 5” which is equal to 10²⁴. In the above example, 4 is the base, 5 is the exponent and the entire setting (The base and exponent) is called power. 

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Keeping in mind the difference between power and exponent, we may conclude that an exponent is a little digit inserted above and to the right of a given integer, whereas the power reflects the entire expression, including the base number and the exponent. When numbers are represented without an exponent, they are in standard form; however, when numbers are written with an exponent, they are in exponential form. The exponent is the little digit in the upper-right corner of the supplied number, whereas the power is the entire statement, which includes both the base and exponent.

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Points to Remember

• The term “Power” is used for the entire context including the base and exponent. The power of a number specifies how many times that number should be multiplied.
• Exponent denotes the number of times a number is used in the multiplication. An exponent is commonly displayed as a raised symbol next to the number or phrase. 
• If the value of an exponent is 0, the value of the base will be 1. If the base is the same and is multiplied, exponents are added.
• If the base is the same and is divided, the exponents are subtracted. If the exponent value is negative, it becomes a denominator and vice versa.
• Exponent is written on the top right corner of any number.
• n exponent is a little digit inserted above and to the right of a given integer, whereas the power reflects the entire expression, including the base number and the exponent. 

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