Page 34 - Maths Skills - 8

32 Maths

3 3 3 4
Example 5: Find the value of .
4 4

3 3 3 4 3
Solution: The rational numbers have the same base .
4 4 4
To find the product we add their powers.
Fact-o-meter

3 3 3 4 3 34 3 7 2187
Thus, . p n q n
4 4 4 4 16384 The reciprocal of is
p
q

3 4 3 6 where n is a positive integer.
Example 6: Evaluate: .
7 7
3 4 3 6 3
Solution: Rational numbers and have the same base .
7 7 7
On comparing their powers, we have 4 < 6.
3 4 3 6 1 1 1 49
Therefore, 3 64 3 2 9 9

7

7

7 7 49

1 2
3

5 9 5 6 Example 8: Evaluate: .
4

Example 7: Find the value of . 2

7 7 1
3
5 Solution:
4
Solution: The rational numbers have the same base .
7 On multiplying the powers,
5 9 5 6 5 96 5 3 125 32 6
Thus, 1 1
7 7 7 7 343 we have
4

4

1 1
=

444444 4096
Example 9: Prove that x = 1.
0
Solution: We know that x ÷ x = x m – n
n
m
If m = n, then x ÷ x = x ÷ x = x n – n = x 0 …(1)
n
n
m
n
For m = n, we can also have
1
x ÷ x = x ÷ x = x × = 1 …(2)
n
n
m
n
n
x n
From (1) and (2), we have x = 1.
0
Example 10: Find the value of x for which  3 4 ×  3 − 7 =  3 2 −x 1
     
7
7
7
3
3
3
3
Solution:    4 ×  3 − 7 =  7 2 −x 1 ⇒  7 4+− ( 7) =  7 2 −x 1
 
 
 
 
7
7