untitled

anbn

a a a a b b b b

( u u u.......u )u( u u u........u )

Formula 4. ̧ ,( z 0 )
¹

·

̈

©

§ b

b

a

b

a

n

n n

We observe, 3

(^33)
2
5
2 2 2
5 5 5
2
5
2
5
2
5
2
5
u u
u u
̧^ u u^
¹
·
̈
©
§
In general,
b
a
b
a
b
a
b
a
b
an
̧^ u u u u
¹
·
̈
©
§ ........ [Successive multiplication of ntimes
b
a
]
n
n
b
a
b b b b
a a a a
u u u u
u u u u
......
......
Formula 5. a^0 1 ,(az 0 )
We have, a a^0
a
a nn
n
n

Again,
a a a a
a a a a
a
a
n
n
u u u u
u u u u
.....
.....
1
?a^0 1.
Formula 6. an ,(az 0 )
n
n n
n
a
a a
a
u
u


1
[multiplying both num. and denom. by an]
n
n n
n n
a
a
a
a
a^1
 
an
1
a^1 n
?an
Remark : n on n
o
a a
a
a  

Formula 7. amn amn

m m m m

mn

a a ua ua u.........ua

ammm.........m

[successive multiplication of n times am]

[in the power, sum of n times of exponent m]

ȏ‹„‘–Š–Š‡…ƒ•‡•‘ˆ—Ǥƒ††‡

—Ž–‹’Ž‹…ƒ–‹‘‘ˆn–‹‡•aȐ

a^1 n

0