The power (1)


   1. Concept of the power

    When we see the picture, we wonder: how many oarsmen participate in the regattas? There are 4 oarsmen in each of the four trawlers, then in total there are 4 x 4 = 16 oarsmen, This can also be written as: 42 and it is read "four to the power of two" .

    The powers are products that are all equal factors.
    Example: 5 x 5 = 52;  6 x 6 x 6 = 63;  7 x 7 x 7 x 7 = 74.

    Do these problems on a paper and write the solution:

1. The power 42 is...

2. The power 24 is...

3. The power 53 is...

4. The power 35 is...

5. The power 32 is...

6. The power 23 is...






    2. - Elements of the power

    In the power 53 we distinguish the base, which is 5 and the exponent, which is 3.
    In this case 53 = 5 x 5 x 5. The base (5) is the number that is repeated in the multiplication. The exponent (3) is the number of times that we must multiply.

1. In the power 73 the 7 is...

2. In the power 73 the 3 is...

3. In 84 the 8 is...

4. In 84 the 4 is...

5. In 52 the 2 is....

6. In 52 the 5 is...


    3. - Perfect Squares  

    The powers with exponent 2 are called perfect squares.
In the picture, we see that the square of 2 (22) is 4, and the square of 3 (32) is 9, and the square of 4 (42) is 16. We can check it by counting the small squares.
    When we studied the multiplication tables, we learned that 7 x 7 = 49. Now we can express it as: 72.

    Exercises:

1. The power 52 =

2. The power 82  =

3. The power 62 =

4. The power 92 =

5. The power 72 =

6. The power 102 =


     

    4. - Squares and cubes

    In the left picture, we see a square of 2 cm long and 2 cm width. In total there are 4 small squares of 1 cm side. 2 cm x 2 cm = 4 cm2

    In the right picture, we see a cube that is 2 cm long, 2 cm wide and 2 cm high. In total, how many small cubes are there? Count them and you will see that there are 8 cubes. 2 x 2 x 2 = 23 = 8. 23 = 8.

    Exercises:

1. 52 =

2. 53 =

3. 63 =

4. 62 =

5. 72 =

6. 73 =



 

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| Educational applications | Mathematics |
In Spanish  | To print

®Arturo Ramo García.-Record of intellectual property of Teruel (Spain) No 141, of 29-IX-1999
Plaza Playa de Aro, 3, 1º DO 44002-TERUEL