Get free PDF of RD Sharma Solutions for Class 7 Maths Exercise 6.1 of Chapter 6 Exponents from the given links. Students who aim to top the examinations they can download the PDFs available here. BYJUâ€™S expert team has solved the questions in such a way that learners can understand easily and comfortably. Students who aim to score high in the Maths of Class 7 are advised to practice all the questions present in the RD Sharma Solutions for Class 7 as many times as possible. This exercise includes definition, the meaning of exponents along with how to read exponents. Here students will thorough about how to express a given number in terms of exponents and why it is introduced and so on.

## Download the PDF of RD Sharma Solutions For Class 7 Chapter 6 – Exponents Exercise 6.1

### Access answers to Maths RD Sharma Solutions For Class 7 Chapter 6 – Exponents Exercise 6.1

**1. Find the values of each of the following:**

**(i) 13 ^{2}**

**(ii) 7 ^{3}**

**(iii) 3 ^{4}**

**Solution:**

(i) Given 13^{2}

13^{2 }= 13 Ã— 13 =169

(ii) Given 7^{3}

7^{3} = 7 Ã— 7 Ã— 7 = 343

(iii) Given 3^{4}

3^{4} = 3 Ã— 3 Ã— 3 Ã— 3

= 81

**2. Find the value of each of the following:**

**(i) (-7) ^{2}**

**(ii) (-3) ^{4}**

**(iii)Â (-5) ^{5}**

**Solution:**

(i) Given (-7)^{2}

We know that (-a) ^{even number}= positive number

(-a)^{ odd number }= negative number

We have, (-7)^{2}Â = (-7) Ã— (-7)

= 49

(ii) Given (-3)^{4}

We know that (-a) ^{even number}= positive number

(-a)^{ odd number }= negative number

We have, (-3)^{4}Â = (-3) Ã— (-3) Ã— (-3) Ã— (-3)

= 81

(iii) Given (-5)^{5}

We know that (-a) ^{even number}= positive number

(-a)^{ odd number }= negative number

We have, (-5)^{5}Â = (-5) Ã— (-5) Ã— (-5) Ã— (-5) Ã— (-5)

= -3125

**3. Simplify:**

**(i) 3 Ã— 10 ^{2}**

**(ii) 2 ^{2}Â Ã— 5^{3}**

**(iii) 3 ^{3}Â Ã— 5^{2}**

**Solution:**

(i) Given 3 Ã— 10^{2}

3 Ã— 10^{2}Â = 3 Ã— 10 Ã— 10

= 3 Ã— 100

= 300

(ii) Given 2^{2}Â Ã— 5^{3}

2^{2}Â Ã— 5^{3}Â = 2 Ã— 2 Ã— 5 Ã— 5 Ã— 5

= 4 Ã— 125

= 500

(iii) Given 3^{3}Â Ã— 5^{2}

3^{3Â }Ã— 5^{2}Â = 3 Ã— 3 Ã— 3 Ã— 5 Ã— 5

= 27 Ã— 25

= 675

**4. Simply:**

**(i)Â 3 ^{2}Â Ã— 10^{4}**

**(ii)Â 2 ^{4}Â Ã— 3^{2}**

**(iii) 5 ^{2}Â Ã— 3^{4}**

** **

**Solution:**

(i)Â Given 3^{2Â }Ã— 10^{4}Â

3^{2Â }Ã— 10^{4}Â = 3 Ã— 3 Ã— 10 Ã— 10 Ã— 10 Ã— 10

= 9 Ã— 10000

= 90000

(ii) Given2^{4}Â Ã— 3^{2}Â

2^{4}Â Ã— 3^{2}Â = 2 Ã— 2 Ã— 2 Ã— 2 Ã— 3 Ã— 3

= 16 Ã— 9

= 144

(iii) Given 5^{2}Â Ã— 3^{4}Â

5^{2}Â Ã— 3^{4}Â = 5 Ã— 5 Ã— 3 Ã— 3 Ã— 3 Ã— 3

= 25 Ã— 81

= 2025

**5. Simplify:**

**(i) (-2) Ã— (-3) ^{3}**

**(ii) (-3) ^{2}Â Ã— (-5)^{3}**

**(iii) (-2) ^{5}Â Ã— (-10)^{2}**

**Solution:**

(i) Given (-2) Ã— (-3)^{3}Â

(-2) Ã— (-3)^{3}Â = (-2) Ã— (-3) Ã— (-3) Ã— (-3)

= (-2) Ã— (-27)

= 54

(ii) Given (-3)^{2}Â Ã— (-5)^{3}Â

(-3)^{2}Â Ã— (-5)^{3}Â = (-3) Ã— (-3) Ã— (-5) Ã— (-5) Ã— (-5)

= 9 Ã— (-125)

= -1125

(iii) Given (-2)^{5}Â Ã— (-10)^{2Â }

(-2)^{5}Â Ã— (-10)^{2Â }= (-2) Ã— (-2) Ã— (-2) Ã— (-2) Ã— (-2) Ã— (-10) Ã— (-10)

= (-32) Ã— 100

= -3200

**6. Simplify:**

**(i) (3/4) ^{2}**

**(ii) (-2/3) ^{4}**

**(iii) (-4/5) ^{5}**

**Solution:**

(i) Given (3/4)^{2}

(3/4)^{2} = (3/4) Ã— (3/4)

= (9/16)

(ii) Given (-2/3)^{4}

(-2/3)^{4} = (-2/3) Ã— (-2/3) Ã— (-2/3) Ã— (-2/3)

= (16/81)

(iii) Given (-4/5)^{5}

(-4/5)^{5} = (-4/5) Ã— (-4/5) Ã— (-4/5) Ã— (-4/5) Ã— (-4/5)

= (-1024/3125)

**7. Identify the greater number in each of the following:**

**(i) 2 ^{5}Â or 5^{2}**

**(ii) 3 ^{4}Â or 4^{3}**

**(iii) 3 ^{5}Â or 5^{3}**

**Solution:**

(i) Given 2^{5}Â or 5^{2}

2^{5}Â = 2 Ã— 2 Ã— 2 Ã— 2 Ã— 2

= 32

5^{2}Â = 5 Ã— 5

= 25

Therefore, 2^{5} >Â 5^{2}

(ii) Given 3^{4}Â or 4^{3}

3^{4}Â = 3 Ã— 3 Ã— 3 Ã— 3

= 81

4^{3Â }= 4 Ã— 4 Ã— 4

= 64

Therefore, 3^{4}Â > 4^{3}

(iii) Given 3^{5Â }or 5^{3}

3^{5}Â = 3 Ã— 3 Ã— 3 Ã— 3 Ã— 3

= 243

5^{3}Â = 5 Ã— 5 Ã— 5

= 125

Therefore, 3^{5} >Â 5^{3}

**Â **

**8. Express each of the following in exponential form:**

**(i) (-5) Ã— (-5) Ã— (-5)**

**(ii) (-5/7) Ã— (-5/7) Ã— (-5/7) Ã— (-5/7)**

**(iii) (4/3) Ã— (4/3) Ã— (4/3) Ã— (4/3) Ã— (4/3)**

**Solution:**

(i) Given (-5) Ã— (-5) Ã— (-5)

Exponential form of (-5) Ã— (-5) Ã— (-5) = (-5)^{3}

(ii) Given (-5/7) Ã— (-5/7) Ã— (-5/7) Ã— (-5/7)

Exponential form of (-5/7) Ã— (-5/7) Ã— (-5/7) Ã— (-5/7) = (-5/7)^{4}

(iii) Given (4/3) Ã— (4/3) Ã— (4/3) Ã— (4/3) Ã— (4/3)

Exponential form of (4/3) Ã— (4/3) Ã— (4/3) Ã— (4/3) Ã— (4/3) = (4/3)^{5}

**9. Express each of the following in exponential form:**

**(i) x Ã— x Ã— x Ã— x Ã— a Ã— a Ã— b Ã— b Ã— b**

**(ii) (-2) Ã— (-2) Ã— (-2) Ã— (-2) Ã— a Ã— a Ã— a**

**(iii) (-2/3) Ã— (-2/3) Ã— x Ã— x Ã— x**

**Solution:**

(i) Given x Ã— x Ã— x Ã— x Ã— a Ã— a Ã— b Ã— b Ã— b

Exponential form of x Ã— x Ã— x Ã— x Ã— a Ã— a Ã— b Ã— b Ã— b = x^{4}a^{2}b^{3}

(ii) Given (-2) Ã— (-2) Ã— (-2) Ã— (-2) Ã— a Ã— a Ã— a

Exponential form of (-2) Ã— (-2) Ã— (-2) Ã— (-2) Ã— a Ã— a Ã— a = (-2)^{4}a^{3}

(iii) Given (-2/3) Ã— (-2/3) Ã— x Ã— x Ã— x

Exponential form of (-2/3) Ã— (-2/3) Ã— x Ã— x Ã— x = (-2/3)^{2Â }x^{3}

**10. Express each of the following numbers in exponential form:**

**(i) 512**

**(ii) 625**

**(iii) 729**

**Solution:**

(i) Given 512

Prime factorization of 512 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

= 2^{9}

(ii) Given 625

Prime factorization of 625 = 5 x 5 x 5 x 5

= 5^{4}

(iii) Given 729

Prime factorization of 729 = 3 x 3 x 3 x 3 x 3 x 3

= 3^{6}

**11. Express each of the following numbers as a product of powers of their prime factors: (i) 36(ii) 675(iii) 392**

**Solution:**

(i) Given 36

Prime factorization of 36 = 2 x 2 x 3 x 3

= 2^{2}Â x 3^{2}

(ii) Given 675

Prime factorization of 675 = 3 x 3 x 3 x 5 x 5

= 3^{3}Â x 5^{2}

(iii) Given 392

Prime factorization of 392 = 2 x 2 x 2 x 7 x 7

= 2^{3}Â x 7^{2}

**12. Express each of the following numbers as a product of powers of their prime factors: (i) 450(ii) 2800(iii) 24000**

**Solution:**

(i) Given 450

Prime factorization of 450 = 2 x 3 x 3 x 5 x 5

= 2 x 3^{2}Â x 5^{2}

(ii) Given 2800

Prime factorization of 2800 = 2 x 2 x 2 x 2 x 5 x 5 x 7

= 2^{4}Â x 5^{2}Â x 7

(iii) Given 24000

Prime factorization of 24000 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5

= 2^{6}Â x 3 x 5^{3}

**13. Express each of the following as a rational number of the formÂ (p/q):**

**(i) (3/7) ^{2}**

**(ii) (7/9) ^{3}**

**(iii) (-2/3) ^{4}**

**Solution:**

(i) Given (3/7)^{2}

(3/7)^{2} = (3/7) x (3/7)

= (9/49)

(ii) Given (7/9)^{3}

(7/9)^{3} = (7/9) x (7/9) x (7/9)

= (343/729)

(iii) Given (-2/3)^{4}

(-2/3)^{4} = (-2/3) x (-2/3) x (-2/3) x (-2/3)

= ((16/81)

**14. Express each of the following rational numbers in power notation:**

**(i) (49/64)**

**(ii) (- 64/125)**

**(iii) (-12/16)**

**Solution:**

(i) Given (49/64)

We know that 7^{2} = 49 and 8^{2}= 64

Therefore (49/64) = (7/8)^{2}

(ii) Given (- 64/125)

We know that 4^{3}Â = 64 and 5^{3}Â = 125

Therefore (- 64/125) = (- 4/5)^{3}

(iii) Given (-1/216)

We know that 1^{3}Â = 1 and 6^{3}Â = 216

Therefore -1/216) = – (1/6)^{3}

**15. Find the value of the following:**

**(i) (-1/2) ^{2}Â Ã— 2^{3}Â Ã— (3/4)^{2}**

**(ii) (-3/5) ^{4}Â Ã— (4/9)^{4}Â Ã— (-15/18)^{2}**

**Solution:**

(i) Given (-1/2)^{2}Â Ã— 2^{3}Â Ã— (3/4)^{2}

(-1/2)^{2}Â Ã— 2^{3}Â Ã— (3/4)^{2Â }= 1/4 Ã— 8 Ã— 9/16

= 9/8

(ii) Given (-3/5)^{4}Â Ã— (4/9)^{4}Â Ã— (-15/18)^{2Â }

(-3/5)^{4}Â Ã— (4/9)^{4}Â Ã— (-15/18)^{2Â }= (81/625) Ã— (256/6561) Ã— (225/324)

= (64/18225)

**16. If a = 2 and b= 3, the find the values of each of the following:**

**(i) (a + b) ^{a}**

**(ii) (a b) ^{b}**

**(iii) (b/a) ^{b}**

**(iv) ((a/b) + (b/a)) ^{a}**

**Solution:**

(i) Consider (a + b)^{a}Â

Given a = 2 and b= 3

(a + b)^{a}Â = (2 + 3)^{2}

= (5)^{2}

= 25

(ii) Given a = 2 and b = 3

Consider, (a b)^{b}Â = (2 Ã— 3)^{3}

= (6)^{3}

= 216

(iii) Given a =2 and b = 3

Consider, (b/a)^{b}Â = (3/2)^{3}

= 27/8

(iv) Given a = 2 and b = 3

Consider, ((a/b) + (b/a))^{a}Â = ((2/3) + (3/2))^{2}

= (4/9) + (9/4)

LCM of 9 and 6 is 36

= 169/36