NCERT Class 7 Mathematics

254 MATHEMATICS

Can you write the appropriate number in the box.

(–11)^2 × (–11)^6 = (–11)

b^2 × b^3 =b (Remember, base is same; bis any integer).

c^3 × c^4 =c (cis any integer)

d^10 × d^20 =d

From this we can generalise that for any non-zero integer a, where m

andnare whole numbers,

am × an =am + n

Caution!

Consider 2^3 × 3^2

Can you add the exponents? No! Do you see ‘why’? The base of 2^3 is 2 and base

of 3^2 is 3. The bases are not same.

13.3.2 Dividing Powers with the Same Base

Let us simplify 3^7 ÷ 34?

37 ÷ 34 =

7

4

3

3

=

3333333

3333

= 3 × 3 × 3 = 3^3 = 37 – 4

Thus 37 ÷ 3^4 =37 – 4

(Note, in 3^7 and 3^4 the base is same and 3^7 ÷ 34 becomes 37– 4)

Similarly,

56 ÷ 5^2 =

5

5

555555

55

6

2 =

×××××

×

= 5 × 5 × 5 × 5 = 5^4 = 56 – 2

or 56 ÷ 52 =56 – 2

Leta be a non-zero integer, then,

a^4 ÷ a^2 =

a

a

aaaa

aa

aa a a

4

2

====^242

or a^4 ÷a^2 =a4 – 2

Now can you answer quickly?

108 ÷ 10^3 =108 – 3 = 10^5

79 ÷ 7^6 =7

a^8 ÷ a^5 =a

Simplify and write in

exponential form:

(i) 2^5 × 2^3

(ii) p^3 × p^2

(iii) 4^3 ×4^2

(iv) a^3 × a^2 × a^7

(v) 5^3 × 5^7 × 5^12

(vi) (– 4)^100 × (– 4)^20

TRY THESE