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# 3 - Powers

Please watch the video and try to fill in the gaps of the TASK 1.

When you power a number you are doing a multiplication of the same number several times.

34 = 3 · 3 · 3 · 3

The terms of a power are called: the base a (the number that is multiplied by itself), and the exponent, b (the number of times that the base is multiplied my itself). ab

And the properties of the power are:

1. Product of powers with the same base: It is another power whose base is the same and whose exponent is the addition of exponents.

am . an = am+n

54 · 53 = 54+3 = 57

2. Division of powers with the same base: It is another power with the same base and whose exponent is the difference between the exponents.

am : a n = am − n

56 : 53 = 56-3 = 53

3. Power of a power: It is another power with the same base and the exponent is the product of the exponents.

(am)n = am · n

(55)4 = 520

4. Multiplication of powers with the same exponent: It is another power with the same exponent, whose base is the product of the bases.

an · b n = (a · b) n

34 · 64 = 184

5. Division of powers with the same exponent: It is another power with the same exponent and whose base is the quotient of the bases.

an : bn = (a : b)n

82 : 22 = 42

6. a0 = 1

7. a1 = a