Page 4 - Matematica_Mathematics - Puterea cu exponent natural a unui numar_The natural exponent power of a number

5. The natural exponent power of a number

By the fourth grade you have learned 4 mathematical
operations: addition, subtraction, multiplication and division. In
the fifth grade, you will learn the fifth mathematical operation,
exponentiation (“ridicarea la putere”).
Exponentiation is a repeated multiplication of the same
factor and its result is called power (“putere”).
Having the addition of equal terms 2 + 2 + 2 + 2 + 2, we
turn it into multiplication: 2 + 2 + 2 + 2 + 2 = 5 × 2 or 2 × 5.

In the case of a multiplication in which the factor 2 is
repeated 5 times, we transform it into exponentiation.

5
2 × 2 × 2 × 2 × 2 = 2 and we read 2 to the fifth power.
The results of those two operations are different, of course, 2 × 5 = 10, and if we perform the
5
multiplication, we will find that 2 equals 32.
5
In the operation 2 , 2 is called base(“baza”), and 5 is the exponent (“exponentul”). In other words, the
base shows you which number is multiplied by itself (the repeating factor) and the exponent indicates how
many times it repeats.

b
Generalizing this operation, we can say that a = a × a × a .... × a
b times
Practice

1. Calculate 5 , then 3 ? Compare the results obtained.
3
5

Remember! • Multiplication is commutative, since 3 × 5 = 5 × 3.
• In the case of exponentiation, changing the place of the
base with the exponent, will bring us to different results, so
5
5 ≠3 .
3
Calculating some of the powers of 4, we get:

0
4 =1 It’s something you’ll need to accept without being demonstrated, because that’s the
way it’s agreed, it’s a convention. In fact, any number raised to the power of 0 equals 1.
a =1
0