Power denotes the repeated multiplication of a factor and the number which is raised to that base factor is the exponent. This is the main difference between power and exponent. For example, 3² is the power where 3 is the base and 2 is the exponent. Learn more about exponent and power here.

In mathematics, the little digit placed above and to the right of any number is known as a superscript. Large numbers are difficult to read, compare and operate because of which they are denoted in the form of small numbers with the help of superscripts. This is done with the help of powers and exponents. Exponents represent the number of times a base number is multiplied. At the same time, power is different from an exponent and consists of two parts known as the base number and the exponent.

Power and Exponent Definition

Power: In Mathematics, the term ‘power’ defines the raising a base number to the exponent. It denotes that the two basic elements of powers are “base number” and “exponent”.  Base Number is defined as a number which is multiplied by itself, whereas the exponent represents the number of times the base number is multiplied. In short, power is a number expressed using the exponents. It implies the repeated multiplication of the same factor. Some special terms 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

Exponent: In mathematics, the exponent is defined as a small number, which is positioned at the up-right of the base number. An exponent can be constants, numbers or any variables. Exponents represent how many times the base number has to be multiplied itself. Usually,l the large numbers are expressed using the exponents. This process is known as the raising to a power.

We can see exponents terms in many scientific notations to denote the large numbers as the powers of 10. Example: the distance between the earth and the sun is expressed in terms of an exponent is 1.50 × 10⁸ km.  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

What are the Differences Between Exponent and Power?

When the numbers are expressed with an exponent, then it is said to be in the exponential form. From the differences between power and exponent provided here, we can say that an exponent is a little digit placed above at the right of a given number, while the power represents the whole expression, containing the base number and the exponent.

Solved Examples

Q.1: Solve 5².5³

Solution: Given,

5².5³

Using exponent rule,

5².5³ = 5²⁺³

= 5⁵

Q.2: Express in exponent form.

(i) 2x2x2x2x2

(ii) 3.3.3.3

(iii) 10.10.10

Solution:

(i) 2x2x2x2x2 = 2⁵

(ii) 3.3.3.3 = 3⁴

(iii) 10.10.10 = 10³

Q.3: Solve 5⁵/5²

Solution: By the law of exponent we know;

x^m/xⁿ = x^m-n

Therefore,

5⁵/5²

= 5^5-2

= 5³