Exercise 11.2

Using laws of exponents, simplify and write the answer in exponential form.

2. Simplify and express each of the following in exponential form.

3. Say true or false and justify your answer.

(i)10 × 1011 = 10011

LHS = 10 × 1011 = 1011+1 = 1012 am×an=am+n

RHS = 10011 = 10211 = 1022 amn=amn

Therefore, 1012 equalnot equal 1022

Thus, the statement is falsetrue

(ii) 23 > 52

LHS = 23 = 2 × × =

RHS = 52 = × 5 =

Therefore, 23 <> 52

Thus, the statement is falsetrue

(iii)23 × 32 = 65

LHS = 23 × 32 = × × 2 × × =

RHS = 65 = × × 6 × 6 ×

Therefore, 23 × 32 not equalequal 65

Thus, the statement is falsetrue

(iv) 30 = 10000 [Since, a0 = 1]

Thus, the statement is truefalse

4. Express each of the following as a product of prime factors only in exponential form.

(i) 108 × 192 = 2 × 2 × × 3 × 3 × × 2 × 2 × 2 × 2 × 2 × 3

= 2 × 3 [am × an = am+n]

(ii) 270 = 2 × × 3 × 3 ×

= 2 × 3 × 5 [am × an = am+n]

= 10 × 3

(iii) 729 × 64 = 3 × × 3 × × 3 × 3 × × × 2 × 2 × 2 ×

= 3 × 2 [am × an = am+n]

= (3 × 2) = 6 [amn = amn]

= 6

(iv) 768 = 2 × 2 × 2 × 2 × 2 × 2 × 3

= 2 × 3 [am × an = am+n]

5. Simplify.

(i) 252×7383×7

= 252×73233×7252×7323+3×7

= 25×2×7325+2×73 ÷ 23×3×723+3×7

= 210×7329×7 = 210−9210+9 × 73−173+1 = × =

(ii)25×52t8103×t4

= 52×52t853×52t8 ÷ 2×53×t42×63×t4

= 52×52×t823×53×t4 = 52+2−3×t8−42352+4−3×t6−423

= 5t4825t216

(iii) 35×105×2557×65

= 35×2×55×5235×3×55×53 ÷ 57×2×3557×2×45

= 35×25×55×5235×24×55×53 ÷ 57×25×3557×23×35

= 35−5×25−5×55+2−7 =