POWERS

1. 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
= 1
2. Any number raised to the first power is always equal to itself. a1
= a
3. 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
.
4. 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:
5. 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
.
6. 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:
1

2. (ab)m
= am
× bm
.
7. 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.
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