Exponent Symbol

Symbols are the main pillars of mathematics that connect one number to the other. There are many commonly used mathematical symbols like a plus(+), minus(-), multiplication (×), division (÷), and so on. One of these symbols, the exponent symbol, is the most important and common one. In this modern era, the importance of knowledge of exponent sign, its variants, usage in mathematics, and how to type it on different software and platforms can’t be denied.

Exponent symbol in mathematics

An exponent refers to the number of times a number is multiplied by itself. The exponent sign was first introduced by Rene Descartes as early as the 17th century in his text named La Géométrie in which he told about its use and how to write. The exponents are the major parts of the algebraic expressions, binomial calculations, and math courses. An exponent symbol is a number or sign placed after and above some other number and symbol. The exponent symbol is also known as the power symbol because it is the power of the digit or number above it.

For example, bx means that x is the power of base “b”. It can also be pronounced like “b raised to the power of X. in this example the “b” is the base and “x” is the exponent.

Calculation of exponents in mathematics

There are several forms of exponents according to the situation and number being used as an exponent. Like addition, multiplication, division solving exponents demands a little bit more understanding of powers. Some of the major and most common calculations of exponents-related problems are discussed below.

Base is an exponential Expression

When we talk about exponential expression, it means to write powers in a short way (short form) which indicate that how many times base is used as a factor.

For example:

81 can be written as 3 × 3 × 3 × 3, which states that 81 = 3 × 3 × 3 × 3 = 34 where 3 is a base and 4 is exponent

For example:

(32)5

Where 32 is base, 5 is an exponent.

Multiplying exponent

There are several possibilities of multiplying exponents, some of which we will discuss here.

If the bases are the same

When we multiply the numbers having the same bases but different power then the exponents add up to each other.

Example:

42 × 44 = 42+4 = 46 = 4096

If the bases are different

If the bases are not the same then first resolve the exponent and then multiply the numbers.

Example:

32 × 43 = 9 × 64 = 576

Adding exponents

If the bases and exponents are same

If the bases and the exponents are the same then count such numbers and multiply them with one such base-exponent digit.

Example:

42 + 42 = 2 × 42 = 2 × 16 = 32

If the bases and exponents are different

The addition of exponent is also different for the different scenarios. If both the bases and exponents are different or the bases are same and exponents are different, the first resolves the exponents with their respective bases separately and then adds them up.

Example:

42 + 25= 4 × 4 + 2 × 2 × 2 × 2 × 2 = 16 + 32 = 48

42 + 43= 4 × 4 + 4 × 4 × 4 = 16 + 64 = 80

Subtracting exponents

Either the bases are the same or different

Subtraction of exponents is also not much difficult. First, you solve the numbers whether they are with the same bases or not, and then apply the simple subtraction to get the answer.

Example:

In this example first 2 raised to the power 3 is solved and then 2 raised to the power 2 is solved and then subtracted.

23 – 22 = 8 – 4 = 4

42 – 23 = 16 – 8 = 8

Division of exponents

The division of the exponents is the opposite of the multiplication of the exponent.

If the bases are the same

In exponential division, if the bases are the same then the answer is also in the exponential form with the same base but the exponents subtracted with each other.

Example:

25 ÷ 23 = 25-3 = 22 = 4

In this only the exponents got subtracted without changing the base.

If the bases are different

If the bases and exponents are different then first resolve them separately and then perform the division.

Example:

43 ÷ 23 = 64 ÷ 8 = 8

Negative exponents

In the negative exponent rule, the number having the negative exponent in the numerator is moved to the denominator as a whole. By doing this the negative exponent becomes the positive and then further calculations will be done.

Example:

(5)-2 = 1/52 = 1/(5 × 5) = 1/25 = 0.04

In this, a with negative exponent -2 become positive by moving to the denominator.

If the base is a fraction

In case if the base is a fraction and the exponent is negative then change the numerator of the base as a denominator and denominator into the numerator to make the exponent positive. In other words change the position of the base fraction.

Example:

(20/10)-7 = (10/20)7

Fractional exponents

If the bases and exponents are the same

Fractional exponents are also called rational or radical exponents. In this situation, if the exponent is in the form of a fraction like 1/2, 2/3, ¾, and so on. If the bases and exponents are the same then first resole the fraction and make a real number exponent and then do further calculations.

Example:

91/2 × 91/2 = 9(1/2+1/2) = 9(1) = 9

In this example, we first take the LCM of the same fractional exponents and after doing this we get the whole number fraction. By doing this we solve the fractional exponents.

If the fractional exponent is x1/n

The general rule in solving x1/n is that simply take the root with the number in the denominator of the fraction.

Example

In this 1/3 becomes the cube root of the base. This is called the nth root rule.

If the exponent is in xm/n form

If both the numerator and denominator of the exponent are not different numbers then split the exponent into two parts, one is the real number(m) and the other into fraction form(1/n).

Example:

We can solve such exponents in this way.

How to type exponent symbol on different software

In this modern age, almost all the writings and calculations are done either on the computer or other software as compared to writing on hard copy. So if one wants to deal with mathematics on these versatile platforms one should know how to type these symbols on them.

  • On the keyboard
    To type the power of something on the normal keyboard press and hold the ctrl + shift and at the same time press the (+) key. By typing this you can get the superscript of the value you want.
  • In Microsoft Word

    If you have to type the power or superscript of any number on word, go to the insert on the top left of the bar and choose the equations option on the top right of the page and there is the option named script, choose it and select the first box to add the superscript.

  • On Mac
    Not everyone uses the same software or device to write on. If someone wants to write the exponent in the apple products like Mac Book,  select the digit or number you want to raise and make exponent then go to the format on the top left and there select the text and then go to the superscript to make the power of something.
  • On PC windows
    The typing of exponent sign on the pc windows is not much different. First go to the insert menu and then select the equations and further go to the script option and then select the superscript box to write the exponent. Then write any number or alphabet you want in the base and exponent boxes.

Fun facts about exponent symbol

Some of the interesting and unique features of the power sign are given below. These are the fun facts of the exponential sign.

Frequently asked questions about exponent symbol

Whenever someone is studying and searching about something, some queries are left unresolved in one’s mind. FAQs are those questions that are most of the time asked by the audience about the related thing. The following are some of the questions frequently asked.

  • When to use power in math?

    If some number has the power or exponent it means that the number is multiplied by itself the exponent times. The exponent symbol is used mostly in algebraic calculations and binomial equations. The base is multiplied by itself like this

    m4 means m will be multiplied by itself 4 times m × m × m × m = m4

  • How to write exponents in fractions 2 power 1/3?

    To type it first type 1/3 and then type 2 and then first select the press ctrl+shift and simultaneously press the= key and type 2, it will become the power of 1/3 as shown.

  • Is the knowledge of exponent signs compulsory in math?

    Mathematics is such a subject in which complete knowledge of all the signs is needed if you want to take command over problems. Since the exponent is the main part of algebra and binomial equations, so it is necessary to have complete knowledge of power signs to solve these algebraic expressions and problems.

  • Are there any shortcut keys for the power symbol?

    Yes, there are various shortcut keys to write power or exponent of some base. These keys are different for different software and one key may not necessarily work for the other software and system. The shortcut keys for the power symbol are discussed above.

Conclusion

There are numerous symbols in mathematics, out of which the exponent symbol is the most important one to know about. Conclusively, if someone is seeking to get to know about the exponent symbol, its usage in mathematics, different rules of power signs in mathematics, then he avails all the things in this article.

Do comment below and express your queries and suggestions so we come next time with quality answers and better content.

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