The DAV Class 6 Maths Book Solutions Pdf and **DAV Class 6 Maths Chapter 3 Worksheet 8 **Solutions of Integers offer comprehensive answers to textbook questions.

## DAV Class 6 Maths Ch 3 WS 8 Solutions

Question 1.

Read aloud:

(a) 5^{2}

(b) 9^{5}

(c) 7^{3}

(d) (- 2)^{4}

(e) (- 10)^{3}

(f) (- 1)^{18}

Solution:

Written answers not required.

Question 2.

Complete the table given below (the first is done for you).

Solution:

Question 3.

Write in power notation.

(a) 4 × 4 × 4

Solution:

4 × 4 × 4 = 4^{3}

(b) (- 2) ×(- 2) × (- 2) × (- 2)

Solution:

(- 2) × (- 2) × (- 2) × (- 2) = (- 2)^{4}

(c) 5 × 5 × 5 × 5 × 5

Solution:

5 × 5 × 5 × 5 × 5 = 5^{5}

(d) (- 10) × (- 10) × (- 10) × ………. 8 times

Solution:

(- 10) × (- 10)× (- 10) × … 8 times = (- 10)^{8}

(e) (- 11) × (- 11) × (- 11)

Solution:

(- 11) × (- 11) × (- 11) = (- 11)^{3}

(f) (- 1) × (- 1) × (- 1) ………….. 33 times

Solution:

(- 1) × (- 1) × (- 1) …………. 33 times = (- 1)^{33}

Question 4.

Write in expanded form:

(a) 2^{5}

Solution:

2^{5} = 2 × 2 × 2 × 2 × 2

(b) 3^{4}

Solution:

3^{4} = 3 × 3 × 3 × 3

(c) (- 7)^{3}

Solution:

(- 7)^{3} = (- 7) × (- 7) × (- 7)

(d) (- 12)^{2}

Solution:

(- 12)^{2} = (- 12) × (- 12)

Question 5.

Compute the following.

(a) 3^{4}

Solution:

3^{4} = 3 × 3 × 3 × 3 = 81

(b) (- 5)^{2}

Solution:

(- 5)^{2} = (- 5) × (- 5) = 25

(c) (- 1)^{78}

Solution:

(- 1)^{78} = 1

(78 is even number

∴ Sign is +)

(d) 11^{3}

Solution:

11^{3} = 11 × 11 × 11

= 1331

(e) (- 4)^{3} × (- 10)^{3} × (- 1)^{789}

Solution:

(- 4)^{3} × (- 10)^{3} × (- 1)^{789}

= – 64 × – 1000 × – 1

[789 is odd number ∴ Sign is (-)]

= – 64000

(f) (50)^{2}

Solution:

(50)^{2} = 50 × 50 = 2500

Question 6.

Find the number which is,

(a) Cube of – 9

(b) Square of 15

(c) 5th power of (- 10)

(d) 19th power of (- 1)

Solution:

(a) Cube of – 9 = (- 9)^{3}

= (- 9) × (- 9) × (- 9)

= – 729

(b) Square of 15 = (15)^{2}

= 15 × 15

= 225

(c) 5th power of (- 10) = (- 10)^{5}

= – 100000

(d) 19th power of (- 1) = (- 1)^{19}

= – 1

Question 7.

Simplify:

(a) 3^{2} + 4^{2}

(b) 2^{3} – 4^{2}

(c) 1^{3} + 2^{3} + 3^{3}

(d) (- 10)^{3} + (- 10)^{2} + (- 10)^{1}

(e) 3^{3} – (- 2)^{3}

(f) (- 1)^{16} + (- 1)^{36} + (- 1)^{7} + (- 1)^{54}

Solution:

(a) 3^{2} + 4^{2}

= 9 + 16

= 25

(b) 2^{3} – 4^{2}

= 8 – 16

= – 8

(c) 1^{3} + 2^{3} + 3^{3}

= 1 + 8 + 27

= 36

(d) (- 10)^{3} + (- 10)^{2} + (- 10)^{1}

= – 1000 + 100 – 10

= – 1010 – 100

= – 910

(e) 3^{3} – (- 2)^{3}

= 27 + 8

= 35

(f) (- 1)^{16} + (- 1)^{36} + (- 1)^{7} + (- 1)^{54}

= 1 + 1 – 1 + 1

= 2

Question 8.

Subtract the cube of (- 2) from the cube of 2.

Solution:

(2 – (- 2) = 8 – (- 8)

= 8 + 8

= 16

Question 9.

Verify:

(a) (- 2)^{5} × (- 2)^{3}

(b) 6^{5} × 6^{4} = 6^{9}

(c) 5^{2} – 3^{2} = 4^{2}

(d) 12^{2} + 5^{2} = 13^{2}

Solution:

(a) (- 2)^{5} × (- 2)^{3}

L.H.S. (- 2)^{5} × (- 2)^{3}

= (- 2)^{5 + 3}

= ( 2)^{8}

R.H.S.

L.H.S. = R.H.S.

Hence Verified

(b) 6^{5} × 6^{4} = 6^{9}

L.H.S.

6^{5} × 6^{4} = 6^{5 + 4}

= 6^{9}

= R.H.S.

L.H.S. = R.H.S.

Hence Verified.

(c) 5^{2} – 3^{2} = 4^{2}

LH.S.

5^{2} – 3^{2}

= 5 × 5 – 3 × 3

= 25 – 9

= 16

R.H.S.

4^{2} = 16

LH.S. = R.H.S.

Hence Verified.

(d) 12^{2} + 5^{2} = 13^{2}

L.H.S. 12^{2} + 5^{2}

= 12 × 12 + 5 × 5

= 144 + 25

= 169

R.II.S.

13^{2} = 13 × 13 = 169

L.H.S. = R.H.S.

Hence Verified

Question 10.

Write ‘True’ or ‘False’ for the following statements.

(a) 3^{4} = 4^{3}

Solution:

False

(b) 9^{7} + 9^{5} = 9^{2}

Solution:

True

(c) (- 5)^{2} x (- 5)^{3} x (- 5) = (- 5)^{6}

Solution:

True

(d) 6^{3} + 6^{2} = 6^{3 + 2}

Solution:

False

(e) Cube of a negative integer is positive.

Solution:

False

(f) (- 1)^{101} = – 1

Solution:

True

(g) 1^{3} = 3

Solution:

False

(h) Cube of a positive integer is negative.

Solution:

False

(i) 3^{2} = 6

Solution:

False

(j) 6th power of a negative integer is positive.

Solution:

True

Question 11.

What power of

(a) 2 is 32

Solution:

32 is 5th power of 2

(b) – 4 is (- 64)

Solution:

– 64 is 3rd power of (- 4)

(c) 10 is 100000

Solution:

100000 is 5th power of 10

(d) (- 5) is – 125

Solution:

– 125 is 3rd power of (- 5)

### DAV Class 6 Maths Chapter 3 Value Based Questions

Question 1.

Ravi and Rahul were good friends. Ravi was a poor boy. He was very much in need of a geometry box. Rahul decided to help him. He bought for him a geometry box costing ₹ 65 from his pocket money. Ravi was very excited to get the new geometry box and thanked Rahul for his caring nature.

(a) Express spending ₹ 65 as an integer.

Solution:

+ 65

(b) Suggest any two ways by which you have helped any of your friends.

Solution:

Sharing lunch and stationery.

Question 2.

In a quiz competition there were 25 questions. 2 marks were allotted to every correct answer and – 1 to every wrong answer. Sheetal attempted 22 questions out of which 2 answers were wrong. The teacher gave her 40 marks. Sheetal went to the teacher and informed her that she has been given more marks. The teacher was happy with Sheetal. She did not deduct her marks.

(a) What is Sheetal’s actual score?

Solution:

No of questions attempted = 22

No. of incorrect answers = 2

∴ No. of correct answers = 22 – 2 = 20

∴ Total marks obtained by Sheetal = 20 (2) + 2 (- 1)

= 40 – 2

= 38

(b) What quality of Sheetal made the teacher happy?

Solution:

Truthful and honesty.