Chapter 13 Exponents and Powers Exercise 13.2

Question 1.
Using laws of exponents, simplify and write the answer in exponential form:

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

Solution:

Question 3.
Say true or false and justify your answer:
(i) 10 × 1011 = 10011
(ii) 23 > 52
(iii) 23 × 32 = 65
(iv) 320 = (1000)0
Solution:
(i) 10 × 1011 = 101+11 = 1012
RHS = 10011 = (102)11 = 1022
1012 ≠ 1022
∴ Statement is false.

(ii) 23 > 52
LHS = 23 = 8
RHS = 522 = 25
8 < 25
∴ 23 < 52
Thus, the statement is false.

(iii) 23 × 32 = 65
LHS = 233 × 32 = 8 × 9 = 72
RHS = 65 = 6 × 6 × 6 × 6 × 6 = 7776
∴ 72 ≠ 7776
∴ The statement is false.

(iv) 30 = (1000)0
⇒ 1 = 1 True [∵ a0 = 1]

Question 4.
Express each of the following as a product of prime factors only in exponential form:
(i) 108 × 192
(ii) 270
(iii) 729 × 64
(iv) 768
Solution:
(i) 108 × 192 = 2 × 2 × 3 × 3 × 3 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3
=28 × 34

(iii) 729 × 64 = 3 × 3 × 3 × 3 × 3 × 3 × 2 × 2 × 2 × 2 × 2 × 2
=36 × 26

Question 5.
Simplify:

Solution:

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