What Are Exponent Rules?

I will give you some apples and ask you to make 3 groups containing 2. Now if you multiply it, The answer you got is 8. You can write the same using numbers like 2  2  2 = 8.

Now I will write it as 23, where 2 is the number of apples in each group and 3 is the total number of times the groups are multiplied. Here 2 is called the base and 3 as an exponent. You can represent this form generally as an.

There are certain rules made to solve the expressions involving exponents easily. These are called exponent rules or Laws of exponents.

What Are Exponent Rules

Let us learn more about exponent rules now. With the help of many examples, we will discuss six of the most important laws of exponents in this article.

Laws or Properties of Exponents:

These are some of the laws or properties of exponents that are needed to be followed while solving the exponents.

  1. Product Rule: As per this rule for real numbers, when bases are the same while doing the multiplication the exponents are added. a) am an = am+n, Eg: 23 22 = 25.
  2. b) am a-n = am-n, Eg: 23 2-2 = 2.
  3. Quotient Rule: As per this rule for real numbers, when bases are the same while doing the division the exponents are subtracted. a) am / an = am-n, when m > n. Eg: 23 / 22 = 2.
  4. b) am / an = 1/an-m, when n > m. Eg: 23 / 25 = 1/22.
  5. Power Rule: As per this rule, when the exponent of an exponent is given for the same base then the exponents are multiplied. (am)n = am n. Eg: (23)2 = 26.
  6. Zero Law of Exponents: As per this rule, when the exponent of a number is zero. Then irrespective of the base value the value of that number is 1. I,e a0 = 1. This law is not applicable for 0 as a base. I.e 00 = undefined.
  7. Power of the Product Rule: As per this rule, If there is a product of two different bases with the same power then it can be written as (a b)n = an bn. Here both a and b are non-zero numbers and n is an integer. Ex: (2  3)2 = 22  32.
  8. Power of the Quotient Rule: As per this rule, If there is a division of two different bases with the same power then it can be written as (a b)n = an bn. Here both a and b is a non-zero numbers and n is an integer. Ex: (2  3)2 = 22  32 = 4/9.
  9. Negative Law of Exponents: As per the law, the reciprocal of an exponent makes the exponent positive. I.e a-m = 1/ am. Eg: 2-6 = 1/26.
  10. Root law of Exponents: According to this law, = x(1/n) and = x(m/n). Eg:  = 3(1/3) and  =  5(2/3)..

Also Read: 12 Characteristics of Economics Students Who Are Successful

Solved Examples:

Example 1:

Solution:  =  = 2,  =

= 2    = ⅖

Example 2: 23 – )0  (-3)3

Solution:  23 = 8, )0 = 1 and (-3)3 = – 27

23 – )0  (-3)3= 8 – 1  (-27) = 8 + 27 = 35.

This is all about the rules or properties of exponents.  For more curious information and solved problems about exponents log on to the Cuemath website.

Exponent laws are also known as properties of exponents. Exponentiation simplifies multiplication and division operations and makes them easier to solve.

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