Page 71 - ICSE Math 7

m
n
Law 2: a ÷ a = a m – n , where a is non-zero rational number and m, n are whole numbers.
2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
3
8
5
Let’s find 2 ÷ 2 = 2 × 2 × 2 × 2 × 2 = 2 . Try This
We can get the same result by subtracting the power of the denominator Find the value of the following.
5
16
(a) 3 ÷ 3 = ______
2 8 6 11
= 2 .
from the power of the numerator, i.e., 5 = 2 8 – 5 3 (b) 5 ÷ 5 = ______
2 4 4
(c) 7 6 ÷ 7 –4 = ______
11 16
mn
m n
Law 3: (a ) = a , where a is non-zero rational number and m, n are whole numbers.
2 3
2
2
2
We have (5 ) = 5 × 5 × 5 = (5 × 5) × (5 × 5) × (5 × 5) = 5 6
6
2 3
We get the same result by multiplying the two powers, i.e., (5 ) = 5 2 × 3 = 5 .
Similarly, we have
3

   6   2  6  3  6  3  6  33+  6  6   3 ×2
6
    =   ×   =   =   =  
7
   7    7   7   7   7   

m
m
m
Law 4: a × b = (ab) , where a and b are non-zero rational numbers and m is a whole number.
We have
2
3
 2 4   4  −2 −2 −2 −   3 3 3 3 
− 
  ×   =  × × ×  ×  × × × 
 3     3 3 3 3   5 5 5 5 
5
 −2 3   −2 3   −2 3   −2 3   −2 3  4  − 2  4
=  ×  ×  ×  ×  ×  ×  ×   ×  =  
=
 3 5   3 5   3 5   3 5   3 5 5   5 
 a  m
m
m
Law 5: a ÷ b =   , where a and b are non-zero rational numbers, and m is any whole

b 
number.
2 3 2 × 2 × 2 2 2 2  2  3
We know = = × × =  
7 3 7 × 7 × 7 7 7 7  7 

0
Law 6: a = 1, where a is any non-zero rational number.

For any non-zero rational number a, we have

5
a
a 5 = a 5 – 5 = a and =  a  5 = (1) = 1. Thus we conclude a = 1.
0
0
5
a 5 a 5  

a 
1
–m
Law 7: a = m, where a is a non-zero rational number and m is any whole number.
a
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