Difference Between Exponent and Power

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. While power is different from an exponent and consists of two parts known as the base number and the exponent.

Power Definition

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 Definition

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 teh sun is expressed in terms of an exponent is 3.84 × 108 million.  Also, there are some important rules while performing some arithmetic operations with exponents. They are:

  • x0 = 1
  • (xm)n = xmn
  • xm × ym = (xy)m
  • xm ÷ ym = (x/y) m
  • xm × xn = xm+n
  • xm ÷ xn = xm-n

key Differences Between Exponent and Power

Power Exponent
Refers to the whole expression representing the repeated multiplication of the same number Represents the number of times the base number is used as a factor in multiplying itself
In \(2^{3}=2\times 2\times 2\), 2 is the base number which is to be multiplied by itself thrice and could be also called as “two to the power of three” or “two to the third power” In \(2^{3}=2\times 2\times 2\), 3 is the exponent which represents the number of times 2 is to be multiplied by itself