Simplify Expressions
in Exponential or
Radical Form
Focus 8 Learning Goal – (HS.N-RN.A.1 & 2, HS.A-SSE.B.3, HS.A-CED.A.2, HS.F-IF.B.4, HS.F-IF.C.8 & 9, and HS.F-LE.A.1) =
Students will construct, compare and interpret linear and exponential function models and solve
problems in context with each model.
4
In addition to level 3,
students make
connections to other
content areas and/or
contextual situations
outside of math.
3
2
1
0
Students will construct, compare, and
interpret linear and exponential
function models and solve problems in
context with each model.
- Compare properties of 2 functions in
different ways (algebraically,
graphically, numerically in tables, verbal
descriptions)
- Describe whether a contextual
situation has a linear pattern of change
or an exponential pattern of change.
Write an equation to model it.
- Prove that linear functions change at
the same rate over time.
- Prove that exponential functions
change by equal factors over time.
- Describe growth or decay situations.
- Use properties of exponents to
simplify expressions.
Students will
construct, compare,
and interpret linear
function models and
solve problems in
context with the
model.
- Describe a situation
where one quantity
changes at a constant
rate per unit interval
as compared to
another.
Students will
have partial
success at a 2
or 3, with help.
Even with help,
the student is
not successful
at the learning
goal.
Review:
When we multiply powers of the same base, the exponents
are added together.
So (91/2)(91/2) should be the same as 91/2+1/2 which is 91 or 9.
But, (3)(3) we also get 9.
Therefore, 91/2 must equal 3!
A Few Rules…
1. You’re allowed to have exponents that are fractions!
2. The denominator of the fraction is the root.
1. A denominator of 2 means a square root.
2. A denominator of 3 means a cube root.
3. A denominator of 10 means a 10th root.
3. The numerator of the fraction is the power.
1. A number with 2/3s power is the cube root of the number
squared.
m/n
Definition of b
For any nonzero real number b, and any
integers m and n with n > 1,
Practice #1
Evaluate 1001/2
The denominator is 2, take the square root of 100.
The numerator is 1, take it to the 1st power.
This means we are taking the square root of 100 to the 1st
power. Which is the same as the square root of 100.
1001/2 = 10
Anything to the ½ power is just the square root of that number.
Practice #2
Evaluate 16 3/2
The denominator is 2, take the square root of 16.
This equals 4.
The numerator is 3, take 4 to the 3rd power.
163/2 = 64
Practice #3
Evaluate 1254/3
The denominator is 3, take the cube root of 125.
This equals 5.
The numerator is 4, take 5 to the 4th power.
1254/3 = 625
Write the radical using rational exponents.
𝟒
𝒙
Since a radical is involved, the exponent will be a fraction.
Remember:
◦ The denominator is the root.
◦ The numerator is the power.
In 4 𝑥 4 is the root = denominator.
1 is the power = numerator.
𝟒
𝒙 = x¼
Practice #4
𝟑
𝒚𝟐
In
3
𝑦2 3 is the root = denominator.
2 is the power = numerator.
𝟑
𝒚𝟐= y2/3
Practice #5
𝟒
𝟏𝟑𝟓
In
4
135 4 is the root = denominator.
5 is the power = numerator.
𝟒
𝟏𝟑𝟓 = 135/4
Apply More Exponent Properties
Simplify:
𝟐
𝟑
𝟑
𝟖
𝒚 ∙𝒚
Same base, add the exponents.
2/ + 3/ = 25/
3
8
24
𝟐𝟓
𝟐𝟒
𝒚
Apply More Exponent Properties
Simplify:
Power to a Power = multiply the exponents
(2/3)(3/4) = (6/12) = ½
y1/2