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RULES OF EXPONENTS
Rule 1 – Exponential Form – A quantity expressed as a number raised to a power. Where the
exponent tells you how many of the bases are being multiplied together.
a5 = a • a • a • a • a
23 = 2 • 2 • 2
Rule 2 – Exponent to zero power is always 1 – The value of any expression raised to the zero
power is always one. (Except zero raised to the zero power is undefined.)
a0 = 1
40 = 1
Rule 3 – Multiplying powers with the same base – copy the base and add the exponents
as • at = a s+t
x3 • x4 = x 3+4  x 7 (this means you have x•x•x•x•x•x•x if you expand it out)
65 • 66 = 6 5+6  611
Rule 4 – Power to power – To raise a number with an exponent to a power, keep the base and
multiply the exponents.
(as)t = ast
(y3)5 = y3•5y15 (this means you have (y3) (y3) (y3) (y3) (y3) if you expand it out)
(72)8 = 72•8716
Rule 5 – Dividing powers with the same base – To divide two numbers with the same base,
keep the base and subtract the exponents
as
x7
st
a
 x 73  x 4
t
3
a
x
xxxxxxx
5
(this
means
if you expand it out)
8
xxxx
57
2

8

8
87
Rule 6 – Negative exponents – Write the exponent as its inverse and make the power

positive.
1
1
1
at  t
x 4  4
4 9  9
a
x
4
Rule 7 –If the bases are different but the exponents are the same, you can multiply the bases
and keep the exponent the same.

at • bt = abt
53 • 73 = 353
35 • 85 = 245
Ex. 1
(x 3 y 2 )(x 2 y 4 )  (x 3  x 2  y 2  y 4 )  x 5 y 6  you can reorder so the x and y are next
to each other
Ex. 2
(5x 5 y 3 )(4 x 6 y 3 )  (5  4  x 5  x 6  y 3  y 3 )  20x11y 6  notice you multiply the
whole numbers
Ex. 3
(x 7 y 4 ) 3  (x 7 ) 3 (y 4 ) 3  x 21y12  you multiply each exponent inside the parentheses
by the power on the outside
Ex. 4
(3x 7 y 5 ) 2  (32 )(x 7 ) 2 (y 5 ) 2  9x14 y10Since the 3 is in the parentheses, it has to be
included
Ex. 5
5(x 6 y 3 ) 6  5(x 6 ) 6 (y 3 ) 6  5x 36 y18 Since the 5 is not in the parentheses, it is not
included
Ex. 6
x 5 y 7z 2
x1 y 5
 2  Do you have more on top than bottom, if so, how many. Where ever
x 4 y 2z 4
z
you have more for each variable is where your answer goes.
Ex. 7
6x 3 y 5
2y 2
 5  When dealing with numbers, treat them as fractions
3x 8 y 3
x
drop the 1 on the bottom. It is not needed.

Ex. 8
5x 6 y 5
x4 y5
5

2
 the
15x y
3
15

1
 , so you can drop the 1.
3
6
2
 . You can
3 1