Download exponent_properties_to_hang

One as
Exponent
Any number
raised to the
power of 1 is
that number
x1 = x
61 = 6
Zero as
Exponent
Any non-zero
number raised to
the power of 0 is
equal to 1.
x0 = 1
70 = 1
Negative One
as Exponent
Write the
base as its
reciprocal
x-1 = 1/x
4-1 = 1/4
Multiplication
of Powers
Powers of the
same base may
be multiplied by
adding their
exponents.
xmxn = xm+n
x2x3 = x2+3 = x5
Division of
Powers
Powers of the same base
may be divided by
subtracting their
exponents.
 x
 n
x

 x
 2
x

m

  x mn


6

62
4
x x


Powers of
Powers
Powers of the
same base may
be raised to
another power by
multiplying their
exponents.
(xm)n = xmn
(x2)3 = x2×3 = x6
Product to a
Power
Apply the
exponent to every
term inside the
parentheses
(xy)n = xnyn
(2y)3 = 23y3 =8y3
Dividing different
bases with the
same exponent
n
x
x
   n
y
 y
n
The exponent gets
applied to both parts
of the fraction –
numerator &
denominator
2
4
4
   2
y
 y
2
16
= 2
𝑦
Negative
Exponents
x-n
=
1/xn
The base gets
written as the
reciprocal and the
power becomes
positive on the
denominator
𝑥
−3
=
1
𝑥3
Different
Bases raised
to the same
power
Multiply the bases
together and
raise the product
to that power
(x)n(y)n = (xy)n
(4)3(t)3 = (4t)3
Commutative
Property of
Addition
As long as the
numbers are all
being added
together, you can
change the order
of your numbers.
a+b+c = a+c+b
6+3+4 = 6+4+3
9+4 = 10+3
13 = 13
Associative
Property of
Addition
As long as the
numbers are all
being added
together, you move
the parentheses to
regroup the
numbers.
(a+b)+c = a+(b+c)
(7+2)+8 = 7+(2+8)
(9)+8 = 7+(10)
17 = 17
Associative
Property of
Multiplication
(a·b)·c = a·(b·c)
As long as the
numbers are all
being multiplied
together, you move
the parentheses to
regroup the
numbers.
(5·9)·2 = 5·(9·2)
(45)·2 = 5·(18)
90 = 90
Commutative
Property of
Multiplication
As long as the
numbers are all
being multiplied
together, you can
change the order
of your numbers.
a·b·c = a·c·b
2·7·5 = 2·5·7
14·5 = 10·7
70 = 70
Distributive
Property
The Distributive
Property lets you
multiply a sum by
multiplying each addend
separately and then add
the products.
a(b+c) = ab+ac
13(2+8) = 13·2+13·8