RD Sharma Class 7 Math 6th Chapter Exponents Exercise 6.2 Solution

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:

 

Leave a Reply

Your email address will not be published. Required fields are marked *