Page 110 - Maths Skills - 7

108 Maths

6. If ‘a’ is a non-zero integer then a = 1
0
5 2 5 2 55×
For example, = 5 2 – 2 = 5 and = = 1
0
5 2 5 2 55×
⇒ 5 = 1.
0
Let us learn more through examples.

Let’s Attempt

Example 1: Simplify the following and express the result in exponential form:
(i) 3 × 3 (ii) 4 ÷ 4 (iii) (7 )
3 2
3
5
7
2
 2 2  2 3  −  1 4  −  1 3  −  1 2
(iv) (– 3) × (– 3) × (– 3) 3 (v)   ×   (vi)    ×   ×  
2
4

3

3


 7
 7
 7
 −  3 7  −  3 2
(vii)   ÷   5  (viii) (3 ) × 5 4
2 2


 5
Solution: (i) 3 × 3 = 3 7 + 3 = 3 [a × a = a m + n ]
3
n
10
m
7
(ii) 4 ÷ 4 = 4 5 – 2 = 4 [a ÷ a = a m – n ]
3
n
5
2
m
(iii) (7 ) = 7 3 × 2 = 7 [(a ) = a m × n ]
m n
3 2
6
(iv) (– 3) × (– 3) × (– 3) = (– 3) 2 + 4 + 3 = (– 3) 9 [a × a = a m + n ]
3
m
4
n
2
 2 2  2 3  2 23+  2 5
m
n
(v)   ×   =   =   [a × a = a m + n ]

3

3
3


3
++
−  1
n
(vi)  −  1   4 ×  −  1  3 ×  −  1  2 =  −  1  432 =    7  9 [a × a = a m + n ]
m








 7
 7
 7
 7
 −  3 7  −  3 2  −  3 7 − 2  −  3 5
(vii)   ÷   5  =    =    [a ÷ a = a m – n ]
m
n


 5
 5
 5
(viii) (3 ) × 5 = 3 2 × 2 × 5 = 3 × 5 4 [(a ) = a m × n ]
m n
2 2
4
4
4
= (3 × 5) = 15 [a × b = (a × b) ]
m
m
m
4
4
Example 2: Simplify the following and express in exponential form:
8
3 × 3 2 × 4 4 7 × a 7
(i) (ii)
3
×
932 7 × a 4
3 × 3 2 × 4 4
8
Solution: (i) 7 × a 7
932 (ii) 4 = 7 8 – 3 × a 7 – 4 [a ÷ a = a m – n ]
×
m
n
3
7 × a
3 × 3 2 × 4 2 2

= [4 = 2 and 9 = 3 , 32 = 2 ] = 7 × a = 7 ·a 3
5
2
5
3
2
5
2
3 × 2 5
= (3 3 – 2 × 2 4 + 2 – 5 ) [a ÷ a = a m – n and a × a = a m + n ]
m
n
n
m
= 3 × 2 = 6
1
1