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0DWK,;;)RUPD

= anum amn

? (am)n amn

Example 1. Find the values (a) 3

2

5

5

(b)

5 5

3

2

3

2



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·

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̧u

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Solution :(a) 3

2

5

5

=

5

1

5

1

52 ^3 5 ^1 1

(b)

5 5

3

2

3

2



̧

¹

·

̈

©

§

̧u

¹

·

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©

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= 1

3

2

3

2

55 0

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Example 2. Simplify : (a)
2 125

5 8 16

5

4

u

u u

(b)

1

2

2 2

3 2 4 2







˜  ˜

n n

n n

Solution: (a)^4375
5

7

3

4

3 5

4 3 4

5 3

4 3 4

5

4

5 2

2

2

5

5

5 2

5 2

2 5

5 2 2

2 125

5 8 16   

u u

u

u

u

u u

u

u u

20 51 u 22 5 u 4

(b)

2

1

2 2

32 2

2 2 2

32 2 2

2 2

32 42 2 2

1

2 2

1

2

 ˜

˜ 

 ˜

˜  ˜



˜  ˜ 









n n

n n

n n

n n

n n

n n

22 4.

2

2

1

2 2

2

2

1

( 3 1 ) 2

2

1

1

32 2

2

˜

˜

˜

˜

 ˜

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˜ 

˜

n

n

n

n

n

n n

Example 3. Show that (ap)qr˜(aq)rp˜(ar)pq 1

Solution : (ap)qr˜(aq)rp˜(ar)pq

1.

[ )

0

( ) ( ) ( )

˜ ˜

˜ ˜

    

  

  

a

a

a a a

a a a (a a

pqprqrpqprqr

pqpr qrpq prqr

pqr qrp rpq  mn ]mn

Activity : Fill in the blank boxes :

(i) 3 u 3 u 3 u 3 3 (ii) 5 u 53 55 (iii)a^2 ua a^3 (iv) 1

4

4

(v)( 5 )^0