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 Page 1


 
 
 
 
 
 
 
Exercise 6.1         Page No: 6.12 
 
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 × 13 =169 
 
(ii) Given 7
3 
7
3
 = 7 × 7 × 7 = 343 
 
(iii) Given 3
4
 
3
4
 = 3 × 3 × 3 × 3 
= 81 
 
2. Find the value of each of the following: 
(i) (-7)
2
 
(ii) (-3)
4
 
(iii)  (-5)
5
 
 
Solution: 
(i) Given (-7)
2 
We know that (-a) 
even number
= positive number 
(-a)
 odd number 
= negative number 
We have, (-7)
2
 = (-7) × (-7) 
= 49 
 
(ii) Given (-3)
4 
We know that (-a) 
even number
= positive number 
(-a)
 odd number 
= negative number 
We have, (-3)
4
 = (-3) × (-3) × (-3) × (-3) 
= 81 
 
(iii) Given (-5)
5
 
Page 2


 
 
 
 
 
 
 
Exercise 6.1         Page No: 6.12 
 
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 × 13 =169 
 
(ii) Given 7
3 
7
3
 = 7 × 7 × 7 = 343 
 
(iii) Given 3
4
 
3
4
 = 3 × 3 × 3 × 3 
= 81 
 
2. Find the value of each of the following: 
(i) (-7)
2
 
(ii) (-3)
4
 
(iii)  (-5)
5
 
 
Solution: 
(i) Given (-7)
2 
We know that (-a) 
even number
= positive number 
(-a)
 odd number 
= negative number 
We have, (-7)
2
 = (-7) × (-7) 
= 49 
 
(ii) Given (-3)
4 
We know that (-a) 
even number
= positive number 
(-a)
 odd number 
= negative number 
We have, (-3)
4
 = (-3) × (-3) × (-3) × (-3) 
= 81 
 
(iii) Given (-5)
5
 
 
 
 
 
 
 
 
We know that (-a) 
even number
= positive number 
(-a)
 odd number 
= negative number 
We have, (-5)
5
 = (-5) × (-5) × (-5) × (-5) × (-5) 
= -3125 
 
3. Simplify: 
(i) 3 × 10
2
 
(ii) 2
2
 × 5
3
 
(iii) 3
3
 × 5
2
 
 
Solution: 
(i) Given 3 × 10
2 
3 × 10
2
 = 3 × 10 × 10 
= 3 × 100 
= 300 
 
(ii) Given 2
2
 × 5
3
  
2
2
 × 5
3
 = 2 × 2 × 5 × 5 × 5 
= 4 × 125 
= 500 
 
(iii) Given 3
3
 × 5
2
 
3
3 
× 5
2
 = 3 × 3 × 3 × 5 × 5 
= 27 × 25 
= 675 
 
4. Simply: 
(i)  3
2
 × 10
4
 
(ii)  2
4
 × 3
2
 
(iii) 5
2
 × 3
4
 
  
Solution: 
(i)  Given 3
2 
× 10
4
   
3
2 
× 10
4
 = 3 × 3 × 10 × 10 × 10 × 10 
= 9 × 10000 
= 90000 
 
Page 3


 
 
 
 
 
 
 
Exercise 6.1         Page No: 6.12 
 
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 × 13 =169 
 
(ii) Given 7
3 
7
3
 = 7 × 7 × 7 = 343 
 
(iii) Given 3
4
 
3
4
 = 3 × 3 × 3 × 3 
= 81 
 
2. Find the value of each of the following: 
(i) (-7)
2
 
(ii) (-3)
4
 
(iii)  (-5)
5
 
 
Solution: 
(i) Given (-7)
2 
We know that (-a) 
even number
= positive number 
(-a)
 odd number 
= negative number 
We have, (-7)
2
 = (-7) × (-7) 
= 49 
 
(ii) Given (-3)
4 
We know that (-a) 
even number
= positive number 
(-a)
 odd number 
= negative number 
We have, (-3)
4
 = (-3) × (-3) × (-3) × (-3) 
= 81 
 
(iii) Given (-5)
5
 
 
 
 
 
 
 
 
We know that (-a) 
even number
= positive number 
(-a)
 odd number 
= negative number 
We have, (-5)
5
 = (-5) × (-5) × (-5) × (-5) × (-5) 
= -3125 
 
3. Simplify: 
(i) 3 × 10
2
 
(ii) 2
2
 × 5
3
 
(iii) 3
3
 × 5
2
 
 
Solution: 
(i) Given 3 × 10
2 
3 × 10
2
 = 3 × 10 × 10 
= 3 × 100 
= 300 
 
(ii) Given 2
2
 × 5
3
  
2
2
 × 5
3
 = 2 × 2 × 5 × 5 × 5 
= 4 × 125 
= 500 
 
(iii) Given 3
3
 × 5
2
 
3
3 
× 5
2
 = 3 × 3 × 3 × 5 × 5 
= 27 × 25 
= 675 
 
4. Simply: 
(i)  3
2
 × 10
4
 
(ii)  2
4
 × 3
2
 
(iii) 5
2
 × 3
4
 
  
Solution: 
(i)  Given 3
2 
× 10
4
   
3
2 
× 10
4
 = 3 × 3 × 10 × 10 × 10 × 10 
= 9 × 10000 
= 90000 
 
 
 
 
 
 
 
 
(ii) Given2
4
 × 3
2
  
2
4
 × 3
2
 = 2 × 2 × 2 × 2 × 3 × 3 
= 16 × 9 
= 144 
 
(iii) Given 5
2
 × 3
4
  
5
2
 × 3
4
 = 5 × 5 × 3 × 3 × 3 × 3 
= 25 × 81 
= 2025 
 
5. Simplify: 
(i) (-2) × (-3)
3
 
(ii) (-3)
2
 × (-5)
3
 
(iii) (-2)
5
 × (-10)
2
 
 
Solution: 
(i) Given (-2) × (-3)
3
   
(-2) × (-3)
3
 = (-2) × (-3) × (-3) × (-3) 
= (-2) × (-27) 
= 54 
 
(ii) Given (-3)
2
 × (-5)
3
  
(-3)
2
 × (-5)
3
 = (-3) × (-3) × (-5) × (-5) × (-5) 
= 9 × (-125) 
= -1125 
 
(iii) Given (-2)
5
 × (-10)
2  
(-2)
5
 × (-10)
2 
= (-2) × (-2) × (-2) × (-2) × (-2) × (-10) × (-10)
 
= (-32) × 100 
= -3200 
 
6. Simplify: 
(i) (3/4)
2
 
(ii) (-2/3)
4
 
(iii) (-4/5)
5
 
 
Solution: 
Page 4


 
 
 
 
 
 
 
Exercise 6.1         Page No: 6.12 
 
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 × 13 =169 
 
(ii) Given 7
3 
7
3
 = 7 × 7 × 7 = 343 
 
(iii) Given 3
4
 
3
4
 = 3 × 3 × 3 × 3 
= 81 
 
2. Find the value of each of the following: 
(i) (-7)
2
 
(ii) (-3)
4
 
(iii)  (-5)
5
 
 
Solution: 
(i) Given (-7)
2 
We know that (-a) 
even number
= positive number 
(-a)
 odd number 
= negative number 
We have, (-7)
2
 = (-7) × (-7) 
= 49 
 
(ii) Given (-3)
4 
We know that (-a) 
even number
= positive number 
(-a)
 odd number 
= negative number 
We have, (-3)
4
 = (-3) × (-3) × (-3) × (-3) 
= 81 
 
(iii) Given (-5)
5
 
 
 
 
 
 
 
 
We know that (-a) 
even number
= positive number 
(-a)
 odd number 
= negative number 
We have, (-5)
5
 = (-5) × (-5) × (-5) × (-5) × (-5) 
= -3125 
 
3. Simplify: 
(i) 3 × 10
2
 
(ii) 2
2
 × 5
3
 
(iii) 3
3
 × 5
2
 
 
Solution: 
(i) Given 3 × 10
2 
3 × 10
2
 = 3 × 10 × 10 
= 3 × 100 
= 300 
 
(ii) Given 2
2
 × 5
3
  
2
2
 × 5
3
 = 2 × 2 × 5 × 5 × 5 
= 4 × 125 
= 500 
 
(iii) Given 3
3
 × 5
2
 
3
3 
× 5
2
 = 3 × 3 × 3 × 5 × 5 
= 27 × 25 
= 675 
 
4. Simply: 
(i)  3
2
 × 10
4
 
(ii)  2
4
 × 3
2
 
(iii) 5
2
 × 3
4
 
  
Solution: 
(i)  Given 3
2 
× 10
4
   
3
2 
× 10
4
 = 3 × 3 × 10 × 10 × 10 × 10 
= 9 × 10000 
= 90000 
 
 
 
 
 
 
 
 
(ii) Given2
4
 × 3
2
  
2
4
 × 3
2
 = 2 × 2 × 2 × 2 × 3 × 3 
= 16 × 9 
= 144 
 
(iii) Given 5
2
 × 3
4
  
5
2
 × 3
4
 = 5 × 5 × 3 × 3 × 3 × 3 
= 25 × 81 
= 2025 
 
5. Simplify: 
(i) (-2) × (-3)
3
 
(ii) (-3)
2
 × (-5)
3
 
(iii) (-2)
5
 × (-10)
2
 
 
Solution: 
(i) Given (-2) × (-3)
3
   
(-2) × (-3)
3
 = (-2) × (-3) × (-3) × (-3) 
= (-2) × (-27) 
= 54 
 
(ii) Given (-3)
2
 × (-5)
3
  
(-3)
2
 × (-5)
3
 = (-3) × (-3) × (-5) × (-5) × (-5) 
= 9 × (-125) 
= -1125 
 
(iii) Given (-2)
5
 × (-10)
2  
(-2)
5
 × (-10)
2 
= (-2) × (-2) × (-2) × (-2) × (-2) × (-10) × (-10)
 
= (-32) × 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) × (3/4)  
= (9/16) 
 
(ii) Given (-2/3)
4
 
(-2/3)
4
 = (-2/3) × (-2/3) × (-2/3) × (-2/3) 
= (16/81) 
 
(iii) Given (-4/5)
5 
(-4/5)
5
 = (-4/5) × (-4/5) × (-4/5) × (-4/5) × (-4/5) 
= (-1024/3125) 
 
7. Identify the greater number in each of the following: 
(i) 2
5
 or 5
2
 
(ii) 3
4
 or 4
3
 
(iii) 3
5
 or 5
3
 
 
Solution: 
(i) Given 2
5
 or 5
2
 
2
5
 = 2 × 2 × 2 × 2 × 2 
= 32 
5
2
 = 5 × 5 
= 25 
Therefore, 2
5
 > 5
2
 
 
(ii) Given 3
4
 or 4
3
 
3
4
 = 3 × 3 × 3 × 3 
= 81 
4
3 
= 4 × 4 × 4 
= 64 
Therefore, 3
4
 > 4
3
 
 
(iii) Given 3
5 
or 5
3
 
3
5
 = 3 × 3 × 3 × 3 × 3 
= 243 
5
3
 = 5 × 5 × 5 
= 125 
Page 5


 
 
 
 
 
 
 
Exercise 6.1         Page No: 6.12 
 
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 × 13 =169 
 
(ii) Given 7
3 
7
3
 = 7 × 7 × 7 = 343 
 
(iii) Given 3
4
 
3
4
 = 3 × 3 × 3 × 3 
= 81 
 
2. Find the value of each of the following: 
(i) (-7)
2
 
(ii) (-3)
4
 
(iii)  (-5)
5
 
 
Solution: 
(i) Given (-7)
2 
We know that (-a) 
even number
= positive number 
(-a)
 odd number 
= negative number 
We have, (-7)
2
 = (-7) × (-7) 
= 49 
 
(ii) Given (-3)
4 
We know that (-a) 
even number
= positive number 
(-a)
 odd number 
= negative number 
We have, (-3)
4
 = (-3) × (-3) × (-3) × (-3) 
= 81 
 
(iii) Given (-5)
5
 
 
 
 
 
 
 
 
We know that (-a) 
even number
= positive number 
(-a)
 odd number 
= negative number 
We have, (-5)
5
 = (-5) × (-5) × (-5) × (-5) × (-5) 
= -3125 
 
3. Simplify: 
(i) 3 × 10
2
 
(ii) 2
2
 × 5
3
 
(iii) 3
3
 × 5
2
 
 
Solution: 
(i) Given 3 × 10
2 
3 × 10
2
 = 3 × 10 × 10 
= 3 × 100 
= 300 
 
(ii) Given 2
2
 × 5
3
  
2
2
 × 5
3
 = 2 × 2 × 5 × 5 × 5 
= 4 × 125 
= 500 
 
(iii) Given 3
3
 × 5
2
 
3
3 
× 5
2
 = 3 × 3 × 3 × 5 × 5 
= 27 × 25 
= 675 
 
4. Simply: 
(i)  3
2
 × 10
4
 
(ii)  2
4
 × 3
2
 
(iii) 5
2
 × 3
4
 
  
Solution: 
(i)  Given 3
2 
× 10
4
   
3
2 
× 10
4
 = 3 × 3 × 10 × 10 × 10 × 10 
= 9 × 10000 
= 90000 
 
 
 
 
 
 
 
 
(ii) Given2
4
 × 3
2
  
2
4
 × 3
2
 = 2 × 2 × 2 × 2 × 3 × 3 
= 16 × 9 
= 144 
 
(iii) Given 5
2
 × 3
4
  
5
2
 × 3
4
 = 5 × 5 × 3 × 3 × 3 × 3 
= 25 × 81 
= 2025 
 
5. Simplify: 
(i) (-2) × (-3)
3
 
(ii) (-3)
2
 × (-5)
3
 
(iii) (-2)
5
 × (-10)
2
 
 
Solution: 
(i) Given (-2) × (-3)
3
   
(-2) × (-3)
3
 = (-2) × (-3) × (-3) × (-3) 
= (-2) × (-27) 
= 54 
 
(ii) Given (-3)
2
 × (-5)
3
  
(-3)
2
 × (-5)
3
 = (-3) × (-3) × (-5) × (-5) × (-5) 
= 9 × (-125) 
= -1125 
 
(iii) Given (-2)
5
 × (-10)
2  
(-2)
5
 × (-10)
2 
= (-2) × (-2) × (-2) × (-2) × (-2) × (-10) × (-10)
 
= (-32) × 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) × (3/4)  
= (9/16) 
 
(ii) Given (-2/3)
4
 
(-2/3)
4
 = (-2/3) × (-2/3) × (-2/3) × (-2/3) 
= (16/81) 
 
(iii) Given (-4/5)
5 
(-4/5)
5
 = (-4/5) × (-4/5) × (-4/5) × (-4/5) × (-4/5) 
= (-1024/3125) 
 
7. Identify the greater number in each of the following: 
(i) 2
5
 or 5
2
 
(ii) 3
4
 or 4
3
 
(iii) 3
5
 or 5
3
 
 
Solution: 
(i) Given 2
5
 or 5
2
 
2
5
 = 2 × 2 × 2 × 2 × 2 
= 32 
5
2
 = 5 × 5 
= 25 
Therefore, 2
5
 > 5
2
 
 
(ii) Given 3
4
 or 4
3
 
3
4
 = 3 × 3 × 3 × 3 
= 81 
4
3 
= 4 × 4 × 4 
= 64 
Therefore, 3
4
 > 4
3
 
 
(iii) Given 3
5 
or 5
3
 
3
5
 = 3 × 3 × 3 × 3 × 3 
= 243 
5
3
 = 5 × 5 × 5 
= 125 
 
 
 
 
 
 
 
Therefore, 3
5
 > 5
3
 
  
8. Express each of the following in exponential form: 
(i) (-5) × (-5) × (-5) 
(ii) (-5/7) × (-5/7) × (-5/7) × (-5/7) 
(iii) (4/3) × (4/3) × (4/3) × (4/3) × (4/3) 
 
Solution: 
(i) Given (-5) × (-5) × (-5) 
Exponential form of (-5) × (-5) × (-5) = (-5)
3
 
 
(ii) Given (-5/7) × (-5/7) × (-5/7) × (-5/7) 
Exponential form of (-5/7) × (-5/7) × (-5/7) × (-5/7) = (-5/7)
4
 
 
(iii) Given (4/3) × (4/3) × (4/3) × (4/3) × (4/3) 
Exponential form of (4/3) × (4/3) × (4/3) × (4/3) × (4/3) = (4/3)
5
 
 
9. Express each of the following in exponential form: 
(i) x × x × x × x × a × a × b × b × b 
(ii) (-2) × (-2) × (-2) × (-2) × a × a × a 
(iii) (-2/3) × (-2/3) × x × x × x 
 
Solution: 
(i) Given x × x × x × x × a × a × b × b × b 
Exponential form of x × x × x × x × a × a × b × b × b = x
4
a
2
b
3
 
 
(ii) Given (-2) × (-2) × (-2) × (-2) × a × a × a 
Exponential form of (-2) × (-2) × (-2) × (-2) × a × a × a = (-2)
4
a
3
 
 
(iii) Given (-2/3) × (-2/3) × x × x × x 
Exponential form of (-2/3) × (-2/3) × x × x × x = (-2/3)
2 
x
3
 
 
10. Express each of the following numbers in exponential form: 
(i) 512 
(ii) 625 
(iii) 729 
Solution:

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FAQs on Exponents (Exercise 6.1) RD Sharma Solutions - Mathematics (Maths) Class 7 (Old NCERT)

1. What are exponents?

Ans. Exponents are mathematical notation that represents how many times a number, known as the base, is multiplied by itself. It is written as a superscript to the right of the base number. For example, in the expression 2^3, 2 is the base and 3 is the exponent. It means that 2 is multiplied by itself three times, resulting in 8.

2. How do exponents work?

Ans. Exponents work by indicating how many times a number should be multiplied by itself. The base number is multiplied by itself the number of times specified by the exponent. For example, in the expression 5^2, the base number 5 is multiplied by itself two times, resulting in 25.

3. What is the rule for multiplying exponents with the same base?

Ans. When multiplying exponents with the same base, you add the exponents together. For example, if you have 2^3 * 2^2, you can rewrite it as 2^(3+2), which simplifies to 2^5. Therefore, 2^3 * 2^2 is equal to 32.

4. What is the rule for dividing exponents with the same base?

Ans. When dividing exponents with the same base, you subtract the exponent of the divisor from the exponent of the dividend. For example, if you have 4^5 / 4^3, you can rewrite it as 4^(5-3), which simplifies to 4^2. Therefore, 4^5 / 4^3 is equal to 16.

5. How do you simplify expressions with exponents?

Ans. To simplify expressions with exponents, you apply the rules of exponents. This includes combining like terms by adding or subtracting the exponents, multiplying exponents with the same base by adding the exponents, and dividing exponents with the same base by subtracting the exponents. By simplifying the expressions, you can obtain a single term or a simplified form of the expression.

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RD Sharma Solutions: Exponents (Exercise 6.1) Class 7 Questions

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