Exponents

Introduction

The exponent of a particular number is essentially the number of times that an individual is multiplying that number with itself. For instance, 45 means that we are multiplying the number four exactly five times. Thus the expanded form of this number is given by 4 * 4 * 4 * 4 * 4. Sometimes an exponent is also referred to as the power of the given number. It does not necessarily have to be an integer. It can either be a negative number, decimal, whole number, positive number, zero, or even fraction. 

Exponent meaning 

As discussed earlier, the exponent of a particular number means the number of times that number has been multiplied by itself. For instance 24 can be written as 2 * 2 * 2 * 2. Here 2 is referred to as the base and 4 is referred to as the power value or exponent value. Generally, xn  means that the number x has been multiplied by itself n times. Here, within the overall term “xn”, x is referred to as the base; n is referred to as the “power” or “exponent”. Moreover, xn is read as x raised to n or x to the power of n. 

Properties and importance of exponents

The importance of exponents lies in the fact that if a number is constantly repeating itself within a product, then it becomes difficult for the mathematician to write that number the given number of times. For instance, one can write 77 more easily as compared to 7 *7 * 7 * 7 *7 * 7 * 7. 

The laws in relation to exponents or properties in relation to exponents are used for solving problems that particularly involve exponents. These specific properties are also considered as major rules of exponents which are specifically used for solving different exponent-related problems. These properties of exponents have been outlined in the following. 

• Quotient law: b^m/ b^n = b^(m+n)
• Zero exponent law: b^0 = 1
• Power of a power law: (b^m)^n = b^(mn)
• Negative Exponent law: b^-n = 1 / b^n
• Power of a Quotient law: (b/c)^m = b^m / c^m
• Power of a product law: (bc)^m = b^m * c^m

Exponent MCQs

The concept of exponent helps in saving time during writing a large product with a number getting repeated several times. MCQ questions are generally formulated from this topic of business mathematics. Some of these have been outlined in the following

1. (34)^3 is given by 

a) 4 

b) 38

c) 312

d) 39

The correct answer is C) which is obtained from the exponent law.

2. The value for 4^2 * 3^2 is 

a) 121

b) 144

c)147

d) 186

The correct answer is b) due to the exponent law. 

 Hence, 42 * 32 = (4 * 3)2 = 122 = 144

3. The value  for 3^-5 * 3^-2 is 

a) 3^-10

b) 3^-14(

c) 3^-7

d) 3^-5

The correct answer is c) and the explanation is of the following manner

3^-5 * 3^-2 = (1 / 3^5) * (1 / 3^2) = (1 / 3^(5 + 2)) = (1 / 3^7) = 3^-7

Exponent Examples

An exponent is a vital concept in mathematics and many examples can be provided in this context. 

Example 1: 6^3 = 6 * 6 * 6 = 216

In other words, the above example can be written as “6 cubed” or “six with the third power” or “six with the power of three”. 

Example 2: 2^6 = 2 * 2 * 2 * 2 * 2 * 2 = 64

In other words, the above example can be written as “2 to the fourth” or “two with the six power” or “two with the power of three”. 

Example 3: 4^3 = 4 * 4 * 4 = 64

In other words, the above example can be written as “4 cubed” or “four with the third power” or “four with the power of three”. 

Conclusion

The overall article has been written on the main topic of exponents. This is a vital concept in business mathematics. Throughout the article, the meaning of exponents and their importance have been discussed. After this, some properties of exponents have been highlighted. Next, some examples about this have been provided. Lastly, MCQ problems that can be commonly faced by the student have been discussed in this article.