Exercise 1.

Look for the term unknown and indicate its name in the following operations:

1.
327 + ....... = 1,208

2.
....... - 4,121 = 626

3.
321 \times ....... = 32,100

4.
28,035 : ....... = 623

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Exercise 2.

Look for the term unknown in the following operations:

1.
4 \times (5 + ...) = 36

2.
(30 - ...) : 5 + 4 = 8

3.
18 \times ... + 4 \times ... = 56

4.
30 - ... : 8 = 25

Exercise 3.

Calculate two different ways of completing the following operations:

1.
17 \times 38 + 17 \times 12 =

2.
6 \times 59 + 4 \times 59 =

3.

(6 + 12) : 3

Exercise 4.

Remove the common factor:

1.
7 \times 5 - 3 \times 5 + 16 \times 5 - 5 \times 4 =

2.
6 \times 4 - 4 \times 3 + 4 \times 9 - 5 \times 4 =

3.

8 \times 34 + 8 \times 46 + 8 \times 20 =

Exercise 5.

Express the following numbers in powers:

1.
50,000

2.
3,200

3.
3,000,000

Exercise 6.

Calculate:

1.
{ 3 }^{ 3 } \times { 3 }^{ 4 } \times 3 =

2.
{ 5 }^{ 7 } : { 5 }^{ 3 } =

3.
(5³)4 {({ 5 }^{ 3 })}^{ 4 }=

4.
{(5 \times 2 \times 3)}^{ 4 } =

5.
{({ 3 }^{ 4 })}^{ 4 } =

6.
{[{({ 5 }^{ 3 })}^{ 4 } ]}^{ 2 } =

7.
{({ 8 }^{ 2 })}^{ 3 }

8.
{({ 9 }^{ 3 })}^{ 2 }

9.
{ 2 }^{ 5 } \times { 2 }^{ 4 } \times 2 =

10.

{ 2 }^{ 7 } : { 2 }^{ 6 } =

11.
{({ 2 }^{ 2 })}^{ 4 } =

12.
{(4 \times 2 \times 3)}^{ 4 } =

13.

{({ 2 }^{ 5 })}^{ 4 }=

14.
{[{({ 2 }^{ 3 })}^{ 4 }]}^{ 0 }=

15.
{({ 27 }^{ 2 })}^{ 5 }=

16.
{({ 4 }^{ 3 })}^{ 2 } =

Exercise 7.

Using powers, carry out the polynomial decomposition of these numbers:

1.
3,257

2.
10,256

3.

125,368

Exercise 8.

Calculate the square roots:

1.

\sqrt { 264 }

2.
\sqrt { 6256 }

3.

\sqrt { 72675 }

Exercise 9.

Calculate:

1.
27 + 3 \times 5 - 16 =

2.
27 + 3 - 45 : 5 + 16 =

3.
(2 \times 4 + 12) (6 − 4) =

4.
3 \times 9 + (6 + 5 - 3) - 12 : 4 =

5.
2 + 5 \times (2 \times 3)³ =

6.
440 − [30 + 6 (19 − 12)] =

7.

2{4 [7 + 4 (5 \times 3 − 9)] − 3 (40 − 8)} =

8.
7 \times 3 + [6 + 2 \times (2³ : 4 + 3 \times 2) - 7 \times \sqrt { 4 }] + 9 : 3 =

 

Solution of exercise 1

Look for the unknown term and indicate its name in the following operations:

1.
327 + ....... = 1,208

addend.

1,208 - 327 = 881

2.
....... - 4,121 = 626

Minuend.

4,121 + 626 = 4,747

3.
321 \times ....... = 32 100

Factor.

32,100 : 321 = 100

4.
28,035: ....... = 623

Divisor.

28,035 : 623 = 45

 

Solution of exercise 2

Look for the unknown term in the following operations:

1.
4 \times (5 + ...) = 36

4

2.
(30 - ...) : 5 + 4 = 8

10

3.
18 \times ... + 4 \times ... = 56

2 and 5

4.
30 - ... : 8 = 25

40

 

Solution of exercise 3

Calculate two different ways of completing the following operations:

1.

17 \times 38 + 17 \times 12 =

17 \times 38 + 17 \times 12 = 646 + 204 = 850

 

2.
6 \times 59 + 4 \times 59 =

6 \times 59 + 4 \times 59 = 354 + 236 = 590

 

3.

(6 + 12) : 3

(6 + 12) : 3 = 18 : 3 = 6

(6 + 12) : 3 = (6 : 3) + (12 : 3) = 2 + 4 = 6

 

Solution of exercise 4

Remove the common factor:

1.
7 \times 5 - 3 \times 5 + 16 \times 5 - 5 \times 4 =

7 \times 5 - 3 \times 5 + 16 \times 5 - 5 \times 4 = 5 (7 − 3 + 16 − 4)

2.
6 \times 4 - 4 \times 3 + 4 \times 9 - 5 \times 4 =

6 \times 4 - 4 \times 3 + 4 \times 9 - 5 \times 4 = 4 (6 − 3 + 9 − 5)

3.

8 \times 34 + 8 \times 46 + 8 \times 20 =

8 \times (34 + 46 + 20)

 

Solution of exercise 5

Express the following numbers in powers:

1.
50,000 = 5 \times { 10 }^{ 4 }

2.
3,200 =
32 \times { 10 }^{ 2 }

3.
3,000,000 =
3 \times { 10 }^{ 6 }

 

Solution of exercise 6

Calculate:

1.
{ 3 }^{ 3 } \times { 3 }^{ 4 } \times 3 = { 3 }^{ 8 }

2.
{ 5 }^{ 7 } : { 5 }^{ 3 } = { 5 }^{ 4 }

3.
{({ 5 }^{ 3 })}^{ 4 } = { 5 }^{ 12 }

4.
{(5 \times 2 \times 3)}^{ 4 } = { 30 }^{ 4 }

5.

{({ 3 }^{ 4 })}^{ 4 } = { 3 }^{ 16 }

6.
{ [{ ({ 5 }^{ 3 }) }^{ 4 }] }^{ 2 } = { ({ (5) }^{ 12 }) }^{ 2 } = { 5 }^{ 24 }

7.
{ ({ 8 }^{ 2 }) }^{ 3 } ={[{({ 2 }^{ 3 })}^{ 2 }]}^{ 3 } = { ({ 2 }^{ 6 }) }^{ 3 } = { 2 }^{ 18 }

8.
{({ 9 }^{ 3 })}^{ 2 } = {[{({ 3 }^{ 2 })}^{ 3 }]}^{ 2 } = {({ 3 }^{ 6 })}^{ 2 } = { 3 }^{ 12 }

9.
{ 2 }^{ 5 } \times { 2 }^{ 4 } \times 2 = { 2 }^{ 10 }

10.

{ 2 }^{ 7 } : { 2 }^{ 6 } = 2

11.
{({ 2 }^{ 2 })}^{ 4 } = { 2 }^{ 8 }

12.
{(4 \times 2 \times 3)}^{ 4 } = { 24 }^{ 4 }

13.

{({ 2 }^{ 5 })}^{ 4 } = { 2 }^{ 20 }

14.
{[{({ 2 }^{ 3 })}^{ 4 }]}^{ 0 } = {({ 2 }^{ 12 })}^{ 0 } = { 2 }^{ 0 }= 1

15.
{({ 27 }^{ 2 })}^{ 5 } = {[{({ 3 }^{ 3 })}^{ 2 }]}^{ 5 } = {({ 3 }^{ 6 })}^{ 5 } = { 3 }^{ 30 }

16.
{({ 4 }^{ 3 })}^{ 2 } = {[{({ 2 }^{ 2 })}^{ 3 }]}^{ 2 } = {({ 2 }^{ 6 })}^{ 2 } = { 2 }^{ 12 }

Solution of exercise 7

Using powers, carry out the polynomial decomposition of these numbers:

1.
3,257

3,257 = 3 \times { 10 }^{ 3 } + 2 \times { 10 }^{ 2 } + 5 \times 10 + 7

2.
10,256

10,256 = 1 \times { 10 }^{ 4 } + 0 \times { 10 }^{ 3 } + 2 \times { 10 }^{ 2 } + 5 \times 10 + 6

3.
125,368

125,368 = 1 \times { 10 }^{ 5 } + 2 \times { 10 }^{ 4 } +5 \times { 10 }^{ 3 } + 3 \times { 10 }^{ 2 } + 6 \times 10 + 8

 

Solution of exercise 8

Calculate the square roots:

1.

2.

3.

 

Solution of exercise 9

Calculate:

1.
27 + 3 \times 5 - 16 =

= 27 + 15 − 16 = 26

2.
27 + 3 - 45 : 5 + 16=

27 + 3 - 9 + 16 = 37

3.
(2 \times 4 + 12) (6 − 4) =

= (8 + 12) (2) = 20 \times 2 = 40

4.
3 \times 9 + (6 + 5 - 3) - 12 : 4 =

= 27 + 8 - 3 = 32

5.
2 + 5 \times (2 \times 3)³ =

= 2 + 5 \times (6)³ = 2 + 5 \times 216 = 2 + 1080 = 1082

6.
440 − [30 + 6 (19 − 12)] =

= 440 − (30 + 6 \times 7)] = 440 − (30 + 42) =

= 440 − (72) = 368

7.
2{4[7 + 4 (5 \times 3 − 9)] − 3 (40 − 8)} =

= 2[4 (7 + 4 \times 6) − 3 (32)] = 2[4 (7 + 24) − 3 (32)]=

2[4 (31) − 3 (32)]= 2 (124 − 96)= 2 (28)= 56

8.

7 \times 3 + [6 + 2 \times (2³ : 4 + 3 \times 2) - 7 \times \sqrt { 4 }] + 9 : 3 =

= 21 + [ 6 + 2 \times (2+ 6) - 14] +3 =

= 21 + ( 6 + 2 \times 8 - 14) +3 =

= 21 + ( 6 + 16 - 14) + 3 =

= 21 + 8 + 3 = 32

 

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.