In this chapter, we provide RD Sharma Class 7 ex 6.1 Solutions Chapter 6 Exponents for English medium students, Which will very helpful for every student in their exams. Students can download the latest RD Sharma Class 7 ex 6.1 Solutions Chapter 6 Exponents Maths pdf, Now you will get step by step solution to each question.

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Textbook | NCERT |

Class | Class 7 |

Subject | Maths |

Chapter | Chapter 6 |

Chapter Name | Exponents |

Exercise | Ex 6.1 |

**RD Sharma Solutions for Class 7 Chapter 6 Decimals** **Ex** **6.1** **Download PDF**

**Chapter 6: Exponents Exercise – 6.1**

**Question: 1**

Find the values of each of the following:

(i) 132

(ii) 73

(iii) 34

**Solution:**

(i) 13^{2} = 13 × 13

= 169

(ii) 7^{3} = 7 × 7 × 7

= 343

(iii) 3^{4 }= 3 × 3 × 3 × 3

= 81

**Question: 2**

Find the value of each of the following:

(i) (-7)^{2}

(ii) (-3)^{4}

(iii) (-5)^{5}

**Solution:**

We know that if ‘a’ is a natural number, then

We have,

(i) (-7)^{2} = (-7) × (-7)

= 49

(ii) (-3)^{4} = (-3) × (-3) × (-3) × (-3)

= 81

(iii) (-5)^{5} = (-5) × (-5) × (-5) × (-5) × (-5)

= -3125

**Question: 3**

Simply:

(i) 3 × 10^{2}

(ii) 2^{2} × 5^{3}

(iii) 3^{3} × 5^{2}

**Solution:**

(i) 3 × 10^{2} = 3 × 10 × 10

= 3 × 100

= 300

(ii) 2^{2} × 5^{3} = 2 × 2 × 5 × 5 × 5

= 4 × 125

= 500

(iii) 3^{3 }× 5^{2} = 3 × 3 × 3 × 5 × 5

= 27 × 25

= 675

**Question: 4**

Simply:

(i) 3^{2} × 10^{4}

(ii) 2^{4} × 3^{2}

(iii) 5^{2} × 3^{4}

**Solution:**

(i) 3^{2 }× 10^{4} = 3 × 3 × 10 × 10 × 10 × 10

= 9 × 10000

= 90000

(ii) 2^{4} × 3^{2} = 2 × 2 × 2 × 2 × 3 × 3

= 16 × 9

= 144

(iii) 5^{2} × 3^{4} = 5 × 5 × 3 × 3 × 3 × 3

= 25 × 81

= 2025

**Question: 5**

Simply:

(i) (-2) × (-3)^{3}

(ii) (-3)^{2} × (-5)^{3}

(iii) (-2)^{5} × (-10)^{2}

**Solution:**

(i) (-2) × (-3)^{3} = (-2) × (-3) × (-3) × (-3)

= (-2) × (-27)

= 54

(ii) (-3)^{2} × (-5)^{3} = (-3) × (-3) × (-5) × (-5) × (-5)

= 9 × (-125)

= -1125

(iii) (-2)^{5} × (-10)^{2 }= (-2) × (-2) × (-2) × (-2) × (-2) × (-10) × (-10)

= (-32) × 100

= -3200

**Question: 6**

Simply:

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

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

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

**Solution:**

**Question: 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) 2^{5} or 5^{2}

2^{5} = 2 × 2 × 2 × 2 × 2

= 32

5^{2} = 5 × 5

= 25

Therefore, 2^{5} 5^{2}

(ii) 3^{4} or 4^{3}

= 3^{4} = 3 × 3 × 3 × 3

= 81

= 4^{3 }= 4 × 4 × 4

= 64

Therefore, 3^{4} 4^{3}

(iii) 3^{5 }or 5^{3}

= 3^{5} = 3 × 3 × 3 × 3 × 3

= 243

= 5^{3} = 5 × 5 × 5

= 125

Therefore, 3^{5} 5^{3}

**Question: 8**

Express each of the following in exponential form

(i) (-5) × (-5) × (-5)

**Solution:**

(i) (-5) × (-5) × (-5) = (-5)^{3}

**Question: 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) x × x × x × x × a × a × b × b × b = x^{4}a^{2}b^{3}

(ii) (-2) × (-2) × (-2) × (-2) × a × a × a = (-2)^{4}a^{3}

(iii) (-2/3) × (-2/3) × x × x × x = (-2/3)^{2 }x^{3}

**Question: 10**

Express each of the following numbers in exponential form

(i) 512

(ii) 625

(iii) 729

**Solution:**

(i) 512 = 2^{9}

(iii) 625 = 5^{4}

(iii) 729 = 3^{6}

**Question: 11**

Express each of the following numbers as a product of powers of their prime factors

(i) 36

(ii) 675

(iii) 392

**Solution:**

(i) 36 = 2 × 2 × 3 × 3

= 2^{2} × 3^{2}

(ii) 675 = 3 × 3 × 3 × 5 × 5

= 3^{3} × 5^{2}

(iii) 392 = 2 × 2 × 2 × 7 × 7

= 2^{3} × 7^{2}

**Question: 12**

Express each of the following numbers as a product of powers of their prime factors

(i) 450

(ii) 2800

(iii) 24000

**Solution:**

(i) 450 = 2 × 3 × 3 × 5 × 5

= 2 × 3^{2} × 5^{2}

(ii) 2800 = 2 × 2 × 2 × 2 × 5 × 5 ×7

= 2^{4} × 5^{2 }× 7

(iii) 24000 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 5 × 5 × 5

= 2^{5} × 3 × 5^{3}

**Question: 13**

Express each of the following as a rational number of the form p/q

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

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

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

**Solution:**

**Question: 14**

Express each of the following rational numbers in power notation

(i) 49/64

(ii) – 64/125

(iii) -12/16

**Solution:**

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

Because 7^{2} = 49 and 8^{2} = 64

(ii) – 64/125 = (- 4/5)^{3}

Because 4^{3} = 64 and 5^{3} = 125

(iii) – (1/216) = – (1/6)^{3}

Because 1^{3} = 1 and 6^{3} = 216

**Question: 15**

Find the value of the following

(i) (-1/2)^{2} × 2^{3} × (3/4)^{2}

(ii) (-3/5)^{4} × (4/9)^{4} × (-15/18)^{2}

**Solution:**

(i) (-1/2)^{2} × 2^{3} × (3/4)^{2 }= 1/4 × 8 × 9/16

= 9/8

(ii) (-3/5)^{4} × (4/9)^{4} × (-15/18)^{2 }= 81/625 × 256/6561 × 225/324 = 64/18225

**Question: 16**

If a = 2 and b= 3, the find the values of each of the followimg

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

(ii) (ab)^{b}

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

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

**Solution:**

(i) (a + b)^{a} = (2 + 3)^{2}

= (5)^{2}

= 25

(ii) (ab)^{b} = (2 × 3)^{3}

= (6)^{3}

= 216

(iii) (b/a)^{b} = (3/2)^{3}

= 27/8

(iv) (a/b + b/a)^{a} = (2/3 + 3/2)^{2}

= 169/36

**All Chapter RD Sharma Solutions For Class 7 Maths**

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