Essential Question: What affect does an exponent have on a fractional
base?
Fractional
Exponents
3
(½)
= 1/8
Bases &
Essential Question: What affect does an exponent have on a fractional
base?
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
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Essential Question: What affect does an exponent have on a fractional
base?
VOCABULARY
Fractional Exponent:
An exponent that is in a fractional form such as ½
_________________________________
Fractional Base:
A base that is in a fractional form such as ¼ .
_________________________________
Essential Question: What affect does an exponent have on a fractional
base?
Quick Review
Essential Question: What affect does an exponent have on a fractional
base?
WHEN MULTIPLYING LIKE BASES,
YOU ADD THE EXPONENTS
a a   a
n
m
n m
FOR EXAMPLE:
3 3   3
2
5
25
3
7
NOW YOU TRY:
4 4   4
6
4
6 4
 4
10
Essential Question: What affect does an exponent have on a fractional
base?
WHEN DIVIDING LIKE BASES, YOU
SUBTRACT THE EXPONENTS.
 an 
n m



a
am 


FOR EXAMPLE:
x5

x3



  x

5 3
 x
2
NOW YOU TRY:
 x 12

 x4



 

x
12 4
x
8
Essential Question: What affect does an exponent have on a fractional
base?
ANY NUMBER RAISED TO THE FIRST
POWER IS ITSELF.
1
a a
FOR EXAMPLE:
3 3
1
NOW YOU TRY:
528921  528921
1
Essential Question: What affect does an exponent have on a fractional
base?
ANY NUMBER RAISED TO THE
ZERO POWER IS ONE.
0
a 1
FOR EXAMPLE:
3 1
0
NOW YOU TRY:
528921  1
0
Essential Question: What affect does an exponent have on a fractional
base?
Excluded Signs
Excluded signs are not included in
the operation. It simply means the
Opposite of…
Ex. -52 = the opposite of 52
Therefore, -52 = -25
Essential Question: What affect does an exponent have on a fractional
base?
Included Signs
Included signs are included in the
operation. It means whatever is
happening to the number is also
happening to the sign.
Ex. (-5)2 = (-5) x (-5)
Therefore, (-5)2 = 25
Essential Question: What affect does an exponent have on a fractional
base?
ANY INTEGER RAISED TO A NEGATIVE EXPONENT
IS THE RECIPROCAL OF THAT ANSWER.
a
1

1
a
FOR EXAMPLE:
-2
3
1
=
9
NOW YOU TRY:
-3
5
1
=
125
Essential Question: What affect does a negative base have on an answer?
What affect does a negative exponent have on an answer?
WHEN RAISING A POWER TO A
POWER, YOU MULTIPLY THE
EXPONENTS
a 
n
m
 a nm
FOR EXAMPLE:
3 
4 6
3
4 *6
3
24
NOW YOU TRY:
4 
3 5
 43*5  415
Essential Question: What affect does an exponent have on a fractional
base?
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Essential Question: What affect does an exponent have on a fractional
base?
Now the NEW
Essential Question: What affect does an exponent have on a fractional
base?
Any exponent with a fractional base effects
both the numerator & denominator.
æaö
a*a
ç ÷ =
èbø
b*b
2
FOR EXAMPLE:
æ2ö
2*2*2
8
=
ç ÷ =
è 5ø
5* 5* 5
125
3
NOW YOU TRY:
æ2ö
ç ÷ =
è3ø
2
4
9
Essential Question: What affect does an exponent have on a fractional
base?
REMEMBER, NEGATIVE EXPONENTS
DO NOT AFFECT THE SIGN OF THE
ANSWER… THEY ONLY AFFECT THE
POSITION OF THE NUMERATOR
AND DENOMINATOR.
Essential Question: What affect does an exponent have on a fractional
base?
Any fraction raised to a negative
exponent is the reciprocal of that
fraction.
a 
 
b 
1
b

a
FOR EXAMPLE:
-2
æ2ö
ç ÷
è 5ø
=
25
4
NOW YOU TRY:
-2
æ 3ö
ç ÷
è4ø
=
16
9
Essential Question: What affect does an exponent have on a fractional
base?
TRY THESE ON YOUR OWN:
æ2ö
ç ÷ =
è3ø
3
-3
æ4ö
ç ÷ =
è 5ø
8
27
125
64
Essential Question: What affect does an exponent have on a fractional
base?
REMEMBER Power Raised to a Power
3 
4 6
3
4 *6
3
24
FOR EXAMPLE:
( 5x y
4
2
)
3
= 125x12 y 6
NOW YOU TRY:
( 4a b c
3
4
11
)
3
=
64a b c
9
12
33
Essential Question: What affect does an exponent have on a fractional
base?
What if the exponent is a fraction?
Essential Question: What affect does an exponent have on a fractional
base?
Power Raised to a Power
No Difference:
1
2
æ 2 4 3ö
3
4
5 ç a b c ÷ = = 5a
è
ø
1
3
3 2 8
bc
Essential Question: What affect does an exponent have on a fractional
base?
Power Raised to a Power
NOW YOU TRY:
1
3
æ 1 3 3ö
3
5
3ç a b c ÷ =
è
ø
1
1
9 1 5
= 3a b c
Essential Question: What affect does an exponent have on a fractional
base?
Quick Write

How does a negative exponent affect a
fraction base?
Essential Question: What affect does an exponent have on a fractional
base?

If a fractional base has an exponent, both the
numerator and denominator are affected by it. If the
exponent is negative, the answer itself will be flip
flopped… That is because a negative exponent is
equivalent to the reciprocal.
Essential Question: What affect does an exponent have on a fractional
base?
THINK / PAIR / SHARE

Step 1 – Spend 20 seconds thinking silently about the
Essential Question.

Step 2 – Spend 30 seconds pairing up with your learning
partner.

Step 3 – Volunteer to share your answer with the class…
Volunteers will receive a Goodybuck.
Essential Question: What affect does an exponent have on a fractional
base?
GIST:
Then write 3-4 sentences to answer the GIST Summary E.Q.