Simplifying
Rational
Exponents
Foldable
Thank you for buying my foldable! © Foresta Math Please stop back to my store and let me know how the game went. http://www.teacherspayteachers.com/Store/Foresta-­‐Math Facebook: Pinterest: https://pinterest.com/forestamath Email: [email protected] Website: http://forestamath.com Polka Dot Frame Shades by Mercedes Hutchens http://www.teacherspayteachers.com/Store/Mercedes-­‐Hutchens Instructions Print or copy page 3 and 4 double sided. Place the paper so the examples are face down. Cut along the dotted lines to create Llaps. Flip and fold the Llaps inwards. Glue the foldable into notes or on a piece of construction paper. Go through the foldable with your students. Rewrite the
expression using
Radical Notation
Rewrite the
expression using
Rational
Exponent
Notation
Quotient Rule
with Rational
Exponents
Product Rule
with Rational
Exponents
Negative
and Zero Rules
with Rational
Exponents
Power Rule with
Rational
Exponents
Rewrite the expression using Radical Notation
Rewrite the expression using Rational Exponent Notation.
Then simplify if possible.
m
n
a = a =
1) 9
1
2
n
m
( a)
n
2) 8
( a)
n
m
2
3
3) x
3
5
4)
5
13
Product Rule with Rational Exponents
5)
7) x ⋅ x
3
5
8)
4
9)
x
x
( )
a
⎛ ⎞
11) ⎜ x ⎟
⎝ ⎠
3
5
1
2
7
10
10)
6
10
⎛ ⎞
12) ⎜ x ⎟
⎝ ⎠
2
3
25
6)
6
x5
6
x2
Negative and Zero Rules with Rational Exponents
m n
3
4
3
m
n
am
= a m−n
n
a
x ⋅ 3 x2
Power Rule with Rational Exponents
= a =a
m
n
Quotient Rule with Rational Exponents
a m ⋅ a n = a m+n
1
5
m
a
⎛ 4⎞
13) ⎜ ⎟
⎝ 9⎠
−3
2
−n
⎛ 1⎞
=⎜ ⎟
⎝ a⎠
n
a0 = 1
⎛ 43 ⎞
14) ⎜ x ⎟
⎝ ⎠
0
( )
7
5
Rewrite the expression using Radical Notation
Rewrite the expression using Rational Exponent Notation.
Then simplify if possible.
m
n
( a)
a = a =
n
1
2
m
n
m
2
3
1) 9 = 2 91
2) 8 = 3 8 2
= 9
= 3 64
=3
=4
( a)
n
3
5
3) x = 5 x 3
4)
5
13 = 13
Product Rule with Rational Exponents
1
5
3
5
7) x ⋅ x = x
4
5
8)
4
1
4
2
=x
11
12
Power Rule with Rational Exponents
( )
a
1
2
⎛ ⎞
11) ⎜ x ⎟ = x
⎝ ⎠
3
5
3
10
25 = 5 = 5
2
3
m
n
2
3
6)
am
= a m−n
n
a
2
3
9)
x
x
7
10
6
10
=x
1
10
( 7)
a
2
3
6
1
⎛ ⎞
12
12) ⎜ x ⎟ = x = x 2
⎝ ⎠
6
10)
6
x
x
5
2
=
x
x
5
6
2
6
3
6
=x =x
Negative and Zero Rules with Rational Exponents
m n
3
4
= a =a
m
n
Quotient Rule with Rational Exponents
x ⋅ x = x ⋅x
3
3
5)
a m ⋅ a n = a m+n
1
5
m
⎛ 4⎞
13) ⎜ ⎟
⎝ 9⎠
−3
2
−n
⎛ 1⎞
=⎜ ⎟
⎝ a⎠
⎛ 9⎞
= ⎜ ⎟
⎝ 4⎠
n
3
2
a0 = 1
0
⎛ 43 ⎞
14) ⎜ x ⎟ = 1
⎝ ⎠
3
⎛ 9⎞
27
= ⎜2 ⎟ =
8
⎝ 4⎠
1
2
5
=7
5
2