The power (2)

1. Powers of 10

In the upper picture, we see that the powers with the base 10 have a common feature: in all cases the result is the unity (1) followed by a number of zeros determined by the magnitude of the exponent.

Exercises:

10^{3} =

10^{5} =

10^{2} =

10^{4} =

10^{7} =

10^{6} =

2. - Powers of 1 and 0

The power 4^{1} = 4; and 12^{1} = 12. In general, a number raised to the exponent 1 is equal to the same number.

The power 4^{0} = 1 and 12^{0} = 1. A number raised to the exponent 0 is equal to 1.

1. The power 5^{1} =

2. The power 5^{0} =

3. The power 72^{0} =

4. The power 72^{1} =

5. The power 7^{1} =

6. The power 7^{0} =

3. - Multiplication and division of powers.

The powers of the same base can be multiplied: 3^{4} x 3^{2} = (3 x 3 x 3 x 3) x (3 x 3) = 3^{6}. 7^{3} x 7^{2} = (7 x 7 x 7) x (7 x 7) = 7^{5}. To multiply powers with the same base, we write the same base and then we add the exponents.

To divide powers with the same base, we write the same base and then we subtract the exponents. 5^{5} : 5^{2} = (5 x 5 x 5 x 5 x 5) : (5 x 5) = 5^{3}. 6^{4} : 6^{2} = (6 x 6 x 6 x 6) : (6 x 6) = 6^{2}.

To divide powers with the same base, we write the same base and then we subtract the exponents.

4. - Problems

You can view the topic of how to solve problems

Problems: 1. You are playing guessing games and Your partner tells you: “think a power that is 16 and its base is 2 and then guess the exponent” 2. How much money did a gentleman spend after 7 weeks if he spends 7 euros per day? 3. How many pencils are in 5 boxes that contain 5 bags, if each bag contains 5 pencils? 4. How many erasers are in 12 pencil cases, if each pencil case contains a dozen of erasers? 5. How many trees are in a forest that has 83 lines and 83 trees in each line? 6. Playing guessing games: think a power that is 1000 and its base is 10. What is the exponent?

1. You are playing guessing games and Your partner tells you: “think a power that is 16 and its base is 2 and then guess the exponent”

2. How much money did a gentleman spend after 7 weeks if he spends 7 euros per day?

3. How many pencils are in 5 boxes that contain 5 bags, if each bag contains 5 pencils?

4. How many erasers are in 12 pencil cases, if each pencil case contains a dozen of erasers?

5. How many trees are in a forest that has 83 lines and 83 trees in each line?

6. Playing guessing games: think a power that is 1000 and its base is 10. What is the exponent?

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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