EXPRESS THE GIVEN EXPRESSION IN INDEX FORM

Example 1 :

Write each number in index form:

a) 2 x 2 x 3 x 3 x 3

b) 2 x 5 x 5

c) 2 x 3 x 3 x 3 x 5

d) 5 x 5 x 7 x 7

e) 2 x 2 x 5 x 5 x 5 x 7

f) 3 x 3 x 7 x 7 x 11 x 11

g) 2 x 2 x 2 x 3 x 3 x 3 x 3

h) 5 x 5 x 5 x 5 x 5 x 5 x 7 x 7 x 7

Solution :

a) 2 x 2 x 3 x 3 x 3

2 is repeating 2 times and 3 is repeating 3 times.

=  2² x 3³

b) 2 x 5 x 5

5 is repeating two times.

=  2x5²

c) 2 x 3 x 3 x 3 x 5

3 is repeating 3 times.

=  2x3³x5

d) 5 x 5 x 7 x 7

5 is repeating 2 times and 7 is repeating 2 times.

=  5²x7²

e) 2 x 2 x 5 x 5 x 5 x 7

2 is repeating 2 times and 5 is repeating 5 times.

=  2²x5³x7

f) 3 x 3 x 7 x 7 x 11 x 11

3 is repeating 2 times, 7 is repeating 2 times and 11 is repeating 2 times.

=  3²x7²x11²

g) 2 x 2 x 2 x 3 x 3 x 3 x 3

2 is repeating 3 times and 3 is repeating 4 times.

=  2³x3⁴

Example 2 :

Write the following in index form with 2 as a base:

a) 16  b) 4  c) 64

Solution :

(a)  16  =  2 x 2 x 2 x 2

Instead of writing 2 four times, we write

16  =  2⁴

(b)  4

4  =  2 x 2

Instead of writing 2 two times, we write

4  =  2²

(c)  64

64  =  2 x 2 x 2 x 2 x 2 x 2

Instead of writing 2 two times, we write

64  =  2⁶

Example 3 :

Write the following in exponent form with 10 as a base :

a) 100 b) 1000 

Solution :

a) 100 

100  =  10 x 10  =  10²

a) 1000 

1000  =  10 x 10 x 10  =  10³

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