DAV Class 6 Maths – Chapter 3 – Worksheet 8

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1. Read aloud

(a) 52

Ans: Five square or Five to the power two.

(b) 95

Ans: Nine to the power five.

(c) 73

Ans: Seven cube or Seven to the power three.

(d) (- 2)4

Ans: Minus Two to the power four

(e) (- 10)3

Ans: Minus Ten cube or Minus Ten to the power three.

(f) (- 1)18

Ans: Minus One to the power eighteen.

2. Complete the table given below.

(a) 75

(b) 93

(c) (- 3)4

(d) (- 1)6

(e) 202

(f) (- 10)7

Ans:

Powered number Base Exponent
75 7 5
93 9 3
(- 3)4 -3 4
(- 1)6 - 1 6
202 20 2
(- 10)7 - 10 7

3. Write in power notation.

(a) 4 x 4 x 4 = 43

(b) (- 2) x (- 2) x (- 2) x (- 2) = (- 2)4

(c) 5 x 5 x 5 x 5 x 5 = 55

(d) (- 10) x (- 10) x (- 10) x ... 8 times = (- 10)8

(e) (- 11) x (- 11) x (- 11) = (- 11)3

(f) (- 1) x (- 1) x (- 1) x ... 33 times = (- 1)33

4. Write the following in expanded form.

(a) 25

Ans: 2 x 2 x 2 x 2 x 2

(b) 34

Ans: 3 x 3 x 3 x 3

(c) (- 7)3

Ans: (- 7) x (- 7) x (- 7)

(d) (- 12)2

Ans: (- 12) x (- 12)

5. Compute the following.

(a) 34

= 3 x 3 x 3 x 3

= 81

Ans: 81

(b) (- 5)2

= (- 5) x (- 5)

= + 25

Ans: + 25

(c) (- 1)78

= (- 1) x (- 1) x (- 1) x...78 times

= + 1

The power 78 is an even number so the the sign will be positive.

Ans: + 1

(d) 113

= 11 x 11 x 11

= 1331

Ans: 1331

(e) (- 4)3 x (- 10)3 x (- 1)789

(- 4)3 = (- 4) x (- 4) x (- 4) = - 64

(- 10)3 = (- 10) x (- 10) x (- 10) = - 1000

(- 1)789 = - 1

(- 4)3 x (- 10)3 x (- 1)789 = (- 64) x (- 1000) x (-1)

= -64000

Ans: - 64000

(f) 502

= 50 x 50

= 2500

Ans: 2500

6. Find the number which is-

(a) Cube of - 9

= (- 9)3

= (-9 ) x (- 9) x (- 9)

= (- 729)

Ans: - 729

(b) Square of 15

= 152

= (15) x (15)

= 225

Ans: 225

(c) 5th power of (- 10)

= (- 10)5

= (- 10) x (- 10) x (- 10) x (- 10) x (- 10)

= - 100000

Ans: - 100000

(d) 19th power of (- 1)

= (- 1)19

The power 19 is an odd number so the the sign will be negative.

= - 1

Ans: - 1

7. Simplify

(a) 32 + 42

= (3 x 3) + (4 x 4)

= 9 + 16

= 25

Ans: 25

(b) 23 - 42

= (2 x 2 x 2) + (4 x 4)

= 8 - 16

= - 8

Ans: - 8

(c) 13 + 23 + 33

= 1 + (2 x 2 x 2) + (3 x 3 x 3)

= 1 + 8 + 27

= 36

Ans: 36

(d) (- 10)3 + (- 10)2 + (- 10)1

= (- 10 x - 10 x - 10) + (- 10 x - 10) + (- 10)

= (- 1000) + (+ 100) + (- 10)

= - 1000 + 100 - 10

= - 900 - 10

= - 910

Ans: - 910

(e) 33 - (- 2)3

= (3 x 3 x 3) - (- 2 x - 2 x - 2)

= (27) - ( - 8)

= 27 + 8

= 35

Ans: 35

(f) (-1)16 + (- 1)36 + (-1)7 + (- 1)54

= (+ 1) + (+ 1) + (- 1) + (+ 1)

= + 1 + 1 - 1 + 1

= + 1 + 1 + 1 - 1

= + 3 - 1

= + 2

Ans: + 2

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

= (2)3 - (- 2)3

= (2 x 2 x 2) - (- 2 x - 2 x - 2)

= (8) - (- 8)

= 8 + 8

= 16

Ans: 16

9. Verify

(a) (- 2)5 x (- 2)3 = (- 2)8

Ans:

LHS RHS
= (- 2)5 x (- 2)3 = (- 2)8
= (-2 x -2 x -2 x -2 x -2) x (-2 x -2 x -2) = (-2 x -2 x -2 x -2 x -2 x -2 x -2 x -2)
= (- 32) x (- 8) = (+ 256)
= (+ 256) = 256
= 256
LHS = RHS
Hence Verified

(b) 65 x 64 = 69

Ans:

LHS RHS
= 65 x 64 = 69
= (6 x 6 x 6 x 6 x 6) x (6 x 6 x 6 x 6) = (6 x 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6)
= 7776 x 1296 = 10077696
= 10077696
= 10077696 = 10077696
LHS = RHS
Hence Verified

(c) 52 - 32 = 42

Ans:

LHS RHS
= 52 - 32 = 42
= (5 x 5) - (3 x 3) = (4 x 4)
= 25 - 9 = 16
= 16
= 16 = 16
LHS = RHS
Hence Verified

(d) 122 + 52 = 132

Ans:

LHS RHS
= 122 + 52 = 132
= (12 x 12) + (5 x 5) = (13 x 13)
= 144 + 25 = 169
= 16
= 169 = 169
LHS = RHS
Hence Verified

10. True or False

(a) 34 = 43 False

34 43
= 3 x 3 x 3 x 3 = 4 x 4 x 4
= 81 = 64
81 ≠ 64
34 ≠ 43

(b) 97 ÷ 95 = 92 True

= 97 ÷ 95

= \(\frac{{9 \times 9 \times 9 \times 9 \times 9 \times 9 \times 9}}{{9 \times 9 \times 9 \times 9 \times 9}}\)

= \(\frac{{\cancel{9} \times \cancel{9} \times \cancel{9} \times \cancel{9} \times \cancel{9} \times 9 \times 9}} {{\cancel{9} \times \cancel{9} \times \cancel{9} \times \cancel{9} \times \cancel{9}}}\)

= 9 x 9

Ans = 92

(c) (- 5)2 x (- 5)3 x (- 5) = (- 5)6 True

(- 5)2 x (- 5)3 x (- 5) (- 5)6
= (- 5 x - 5) x (- 5 x - 5 x - 5) x (- 5) = (- 5 x - 5 x - 5 x - 5 x - 5 x - 5)
= (+ 25) x (- 125) x (- 5) = (+ 15625)
= (- 3125) x (- 5)
= (+ 15625)
15625 = 15625
(- 5)2 x (- 5)3 x (- 5) = (- 5)6

(d) 63 + 62 = 63+2 False

63 + 62 63+2
= (6 x 6 x 6) + (6 x 6) = 65
= 216 + 36 = (6 x 6 x 6 x 6 x 6)
= 252 = 7776
252 ≠ 7776
63 x 62 ≠ 63+2

(e) Cube of a negative integer is positive. False

= (- 2)3

= (-2 x -2 x -2)

= -8

Cube of a negative integer is Negative

(f) (- 1)101 = - 1 True

= (- 1)101

= - 1

101 is an odd number so the final solution will be a Negative integer.

(g) 13 = 3 False

= 13

= 1 x 1 x 1

= 1

13 = 1

(h) Cube of a positive integer is negative. False

= 23

= (2 x 2 x 2)

= 8

Cube of a positive integer is positive.

(i) 32 = 6 False

= 32

= (3 x 3)

= 9

32 = 9

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

= (- 1)6

= (-1 x -1 x -1 x -1 x -1 x -1)

= 1

6 is an even number so the final solution will be a positive integer.

11. What power of-

(a) 2 is 32

\[ 2^? = 32 \]

\[ \begin{array}{c|c} 2 & 32 \\ \hline 2 & 16 \\ \hline 2 & 8 \\ \hline 2 & 4 \\ \hline 2 & 2 \\ \hline & 1 \\ \end{array} \] \[ 32 = 2 \times 2 \times 2 \times 2 \times 2 \] \[ 32 = 2^5 \]

Ans = Fifth

(b) - 4 is - 64

\[ (- 4)^? = -64 \]

\[ \begin{array}{c|c} 4 & 64 \\ \hline 4 & 16 \\ \hline 4 & 4 \\ \hline & 1 \\ \end{array} \] \[ -64 = (- 4) \times (- 4) \times( - 4) \] \[ - 64 = (- 4)^3 \]

Ans = Third

(c) 10 is 100000

\[ 10^? = 100000 \]

\[ \begin{array}{c|c} 10 & 100000 \\ \hline 10 & 10000 \\ \hline 10 & 1000 \\ \hline 10 & 100 \\ \hline 10 & 10 \\ \hline & 1 \\ \end{array} \] \[ 100000 = 10 \times 10 \times 10 \times 10 \times 10 \] \[ 100000 = 10^5 \]

Ans = Fifth

(d) (- 5) is 125

\[ (-5)^? = -125 \]

\[ \begin{array}{c|c} 5 & 125 \\ \hline 5 & 25 \\ \hline 5 & 5 \\ \hline & 1 \\ \end{array} \] \[ (-125) = (-5) \times (-5) \times (-5) \] \[ (-125) = (-5)^3 \]

Ans = Third