Properties Of Exponents Cheat Sheet Page 2
ADVERTISEMENT
1
2Properties of Exponents Cheat Sheet
Name_____________________________________
Multiplication Property:
EX w/ numbers:
EX w/ variables:
EX w/ num. and variables:
3
5
3+5
8
2
10
2+10
12
2
3
5
· 3
· x
y · 4x
3
=
3
= 3
x
=
x
= x
2x
y
=
n
m
(n+m)
· b
b
= b
2+3
1+5
5
6
·y
2·4·x
= 8x
y
Add exponents if bases are the
same
Power Property:
EX w/ numbers:
EX w/ variables:
EX w/ num. and variables:
3 · 4
3 · 11
3
4
12
3
11
33
4
8
4
(5
)
=
5
= 5
(y
)
=
y
= y
(6x
y
z)
=
n · m
n
m
(b
)
= b
4
4·4
8·4
4
6
x
y
z
=
16
32
4
1296x
y
z
Multiply exponents when they are
inside and outside parenthesis
Distribute the exponent to ALL
terms!
Division Property:
EX w/ numbers:
EX w/ variables:
EX w/ num. and variables:
12
12-5
7
17
17-6
11
10
10-4
6
3
=
3
= 3
y
=
y
= y
3x
=
1 x
= 1 x
n
(n-m)
b
= b
5
6
4
3
y
9x
3
3
m
b
Subtract top exponent minus
bottom exponent
Simplify all fractions!
Zero Property:
EX w/ numbers:
EX w/ variables:
EX w/ num. and variables:
0
0
2
4
0
100
=
1
(xy)
=
1
(3a
b
)
=
1
0
b
= 1
2
4
0
3(a
b
)
=
3·1 = 3
Any number raised to the zero
power is equal to 1
Negative Exponent Property:
EX w/ numbers:
EX w/ variables:
EX w/ num. and variables:
-4
-6
-10
2
3
=
1
x
=
1
16x
=
8x
= 8
-n
n
4
6
-2
10
8
b
= 1 and 1 = b
3
x
2x
x
x
n
-n
b
b
If the exponent is negative move
the term to the opposite side and
make the exponent positive
Simplify all fractions!
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education