The power
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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: 4^{2} and it is read "four to the power of two" .
The powers are products that are all equal factors.
Example: 5 x 5 = 5^{2}; 6 x 6 x 6 = 6^{3};
7 x 7 x 7 x 7 = 7^{4}.
Do these problems on a paper and write the solution:
1. The power 4^{2} is... 

2. The power 2^{4} is... 

3. The power 5^{3} is... 

4. The power 3^{5} is... 

5. The power 3^{2} is... 

6. The power 2^{3} is... 
2.  Elements of the power
In the power
5^{3} we distinguish the base, which is 5 and the exponent, which is 3.
In this case 5^{3} = 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 7^{3} the 7 is... 

2. In the power 7^{3} the 3 is... 

3. In 8^{4} the 8 is... 

4. In 8^{4} the 4 is... 

5. In 5^{2} the 2 is.... 

6. In 5^{2} 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 (2^{2}) is 4, and the square of 3 (3^{2}) is 9, and the square of 4 (4^{2}) 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: 7^{2}.
Exercises:
1. The power 5^{2} = 

2. The power 8^{2} = 

3. The power 6^{2} = 

4. The power 9^{2} = 

5. The power 7^{2} = 

6. The power 10^{2} = 
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 cm^{2}
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. 2^{3} = 8.
Exercises:
1. 5^{2} = 

2. 5^{3} = 

3. 6^{3} = 

4. 6^{2} = 

5. 7^{2} = 

6. 7^{3} = 
 Educational applications 
Matematics 
In Spanish  Interactive
®Arturo Ramo García.Record of intellectual property of Teruel (Spain)
No 141, of 29IX1999
Plaza Playa de Aro, 3, 1º DO 44002TERUEL