Exercise 6.2
1. Using laws of exponents, simplify and write the answer in exponential form:
(i) 23 × 24 × 25
(ii) 512 ÷ 53
(iii) (72)3
(iv) (32)5 ÷ 34
(v) 37 × 27
(vi) (521 ÷ 513) × 57
Solution:
(i) Given 23×24×25
We know that first law of exponents states that am×an×ap = a(m+n+p)
Therefore above equation can be written as 23 × 24 × 25=2(3+4+5)
=212
(ii) Given 512 ÷ 53
According to the law of exponents we have am÷an = am+n
Therefore given question can be Written as 512÷ 53 = 512-3 =59
(iii) Given (72)3
According to the law of exponents we have (am)n = amm
Therefore given question can be written as (72)3=76
(iv) Given (32)5÷34
According to the law of exponents we have (am)n = amm
Therefore (32)5÷34 = 310 ÷34
According to the law of exponents we have am÷an= am+n
(v) Given 37 × 27
We know that law if exponents states that am bm= (a×b)m
3727=(3×2)7 = 67
(vi) Given
(521 ÷ 513) × 57
According to0 the law of exponents we have am÷an=am-n
= 5 (21-13) ×57
= 58×57
According to the law of exponents we have aman=am+n
= 5(8+7) =515
2. Simplify and express each of the following in exponential form
Solution:
3. Simplify and express each of the following in exponential form
Solution:
(iii) Given (5/2)6 × (5/2)2
= (5/2)6+2 [According to the law of components we have am×an = a m+n]
= (5/2)8
(iv) given (2/3)5 × (3/5)5
= (2/5)5 [Since law of exponents state that am×bm = (a×b)m]
4. Write 9 × 9 × 9 × 9 × 9 in exponential form with base 3
Solution:
9 × 9 × 9 × 9 × 9 = (9)5 = (32)5
= 310
5. Simplify and write each of the following in exponential form
Solution:
6. Simplify
Solution:
7. Find the value of n in each of the following: