How to Divide Exponents

How to Divide Exponents

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So, in layman terms, exponent of a number is basically referred to as the power of that number. So, for example, we have often seen this phrase in mathematics “2 to the power 4”. So, this is nothing but 24. This generally means that 2 is multiplied by itself 4 times. So, the general expression could be written as 2×2×2×2
Exponents are basically used to reduce the length of an algebraic expression. We know how tedious would it be if we had to write “2 to the power 10” in the general form without the exponent. 210 is a very simple and less tedious way to write this.
Now, let’s consider the exponent case of 24. In this case, 2 is referred to as the "base," while 4 is referred to as the "exponent" or "power." In the term xn:

  • n is the exponent or power
  • x is called the base

Properties of Exponents

When dealing with exponents, it is necessary to apply the properties of exponents or the rules of exponents in order to solve the problem. These characteristics are also referred to as major exponents rules, which must be observed when solving exponent problems. The next section discusses the properties of exponents.

  • The Product Law states that am×an = am + n
  • The Law of Quotients states that aman = am  n
  • The Law of the Zero Exponent is as follows: a0 = 1
  • The Law of the Negative Exponent states that am = 1am
  • The Law of the Power of a Power is as follows: (am)n = am×n
  • The Power of a Product is defined as (ab)m = am×bm
  • The Power of a Quotient is defined as (ab)m = ambm

Division Properties of Exponents

Some division properties of exponents are:

  • The Law of Quotients states that aman = am  n
  • The Power of a Quotient is defined as (ab)m = ambm

Free printable Worksheets

Exercises for Division Property of Exponents

1) 22x72x3=

2) 959=

3) 6x62x3=

4) 24x73x3=

5) 18x62x2=

6) 16x64x3=

7) 262=

8) 10x82x3y2=

9) 18x73x4y3=

10) 353=

 
1) 22x72x3= 222 x(73) =11x4
2) 959= 9(51) =94
3) 6x62x3= 62 x(63) =3x3
4) 24x73x3= 243 x(7(3)) =8x4
5) 18x62x2= 182 x(6(2)) =9x4
6) 16x64x3= 164 x(63) =4x3
7) 262= 2(61) =25
8) 10x82x3y2= 102 x(8(3))y2 =5x5y2
9) 18x73x4y3= 183 x(7(4))y3 =6x3y3
10) 353= 3(51) =34

Division Property of Exponents Quiz