Unit 2 powers
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I.E.S. MARÍA BELLIDO - BAILÉN BILINGUAL SECTION – MARÍA ESTHER DE LA ROSA POWERS 1. DEFINITION OF POWER Power or Exponent tells how many times a number is multiplied by itself. In the expression a n , the exponent is “n” and “a” is the base. Example: In 2 4 , 4 is the exponent. It indicates that 2 is going to be multiplied by itself 4 times. 2 4 = 2 × 2 × 2 × 2 = 16 If a number “b” is raises to the second power, we say it is “b squared“, b 2 (this number is known like a square number) If a number “b” is raises to the third power, we say it is “b cubed”, b 3 2. POWER PROPERTIES 1. Any number (except zero) raise to the power of 0 is equal to 1. a 0 = 1 2. Any number raised to the first power is always equal to itself. a 1 = a
Transcript of Unit 2 powers
I.E.S. MARÍA BELLIDO - BAILÉN
BILINGUAL SECTION – MARÍA ESTHER DE LA ROSA
POWERS
1. DEFINITION OF POWER
Power or Exponent tells how many times a number is multiplied by itself. In the expression an, the exponent is “n” and “a” is the base.
Example: In 24, 4 is the exponent. It indicates that 2 is going to be multiplied by itself 4 times. 24 = 2 × 2 × 2 × 2 = 16
If a number “b” is raises to the second power, we say it is “b squared“, b2 (this number is known like a square number)
If a number “b” is raises to the third power, we say it is “b cubed”, b3
2. POWER PROPERTIES
1. Any number (except zero) raise to the power of 0 is equal to 1. a0 = 12. Any number raised to the first power is always equal to itself. a1 = a3. Product of Powers Property: This property states that to multiply powers
having the same base, add the exponents.That is, for a real number non-zero a and two integers m and n:
am × an = am+n.
Quotient of Powers Property: This property states that to divide powers having the same base, subtract the exponents.
That is, for a non-zero real number a and two integers m and n:
4. Power of a Power Property: This property states that the power of a power can be found by multiplying the exponents.That is, for a non-zero real number a and two integers m and n:
(am)n = amn.
5. Power of a Product Property: This property states that the power of a product can be obtained by finding the powers of each factor and multiplying them. That is, for any two non-zero real numbers a and b and any integer m:
(ab)m = am × bm.
6. Power of a Quotient Property: This property states that the power of a quotient can be obtained by finding the powers of numerator and denominator and dividing them. That is, for any two non-zero real numbers a and b and any integer m
.
3. NEGATIVE EXPONENTS
A negative exponent just means that the base is on the wrong side of the fraction line, so you need to flip the base to the other side.
For example: x–2 (x to the minus two) just means "x2, but underneath, as in
1/(x2)".
4. SQUARE ROOTS
Finding the square root is the opposite of finding square numbers. You can find a square root:
1. Using the powers: Example: because 2. With calculator 3. Using an algorithm.
If you are using integer numbers, you must remember the following propertie: √16 = ± 4 because 42 = 16 and (- 4)2 = 16. √-9 doesn´t exist because neither 3 nor -3 to the square are 9.
