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Laws of Exponents

PrintThe continued product of a number multiplied with itself a number of times can be written as the number raised to the power a natural number, equal to the number of times the number is multiplied with itself.


To make calculations easier, we have few rules or laws of exponents:
•    Multiplying Powers with the same base
•    Dividing Powers with the same base
•    Power with Exponent zero
•    Power of a Power
•    Multiplying Powers with the same exponents
•    Dividing Powers with the same exponents

Let’s discuss each one of them in detail:


Law 1: Multiplying Powers with the same base


If ‘a’ is any non – zero rational number and m, n are natural numbers, then
am x an = am + n

Also, If ‘a’ is any non – zero rational number and m, n, p are natural numbers, then

am x an x ap = am + n + p

Example: Simplify: 32 x 35

= 32 + 5
= 37



Law 2: Dividing Powers with the same base


If ‘a’ is any non – zero rational number and m, n are natural numbers such that m > n, then
                                                                               am ÷ an = am – n or am = am – n
                                         exp_1                                                                 an


Example: Simplify: 912 ÷ 910

= 912 – 10
= 92



Law 3: Power with exponent zero

If ‘a’ is any non – zero rational number raise to power 0, then it is equal to 1
a0 = 1

Example: 73 ÷ 73

= 73 – 3
= 70
= 1



Law 4: Power of a Power

If ‘a’ is any rational number different from zero and m, n are natural numbers, then
(am)n = am x n = (an)m

Example: Simplify: (23)4 = 23 x 4 = 212



Law 5: Multiplying Powers with the same exponents

If a, b are non – zero rational numbers and n is a natural number, then
an x bn = (ab)n

Also, If a, b, c are non – zero rational numbers and n is a natural number, then

an x bn x cn = (abc)n

Example: 25 x 35

= (2 x 3)5
= 65



Law 6: Dividing Powers with the same exponents

If a and b are non – zero rational numbers and n is a natural number, then
                                                                                              an = a n
                                             exp_3                                  bn = b

Example: (2/3)2

= (2 x 2)/(3 x3)
= 4/9
       

Now try it yourself!  Should you still need any help, click here to schedule live online session with e Tutor!



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