1. I.E.S. MARÍA BELLIDO - BAILÉN
BILINGUAL SECTION – MARÍA ESTHER DE LA ROSA
UNIT 2. 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
● 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:
(ab)m = am × bm.
7. Power of a Quotient Property: This property states that the power of

2. 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
.