Download GUIDED NOTES – Lesson 4-1

GUIDED NOTES – Lesson 4-1
Rational Exponents and Radical Expressions
Name: ______________________ Period: ___
OBJECTIVE: I can simplify and convert radical expressions and rational exponents.
Sometimes fractional exponents are used to represent power of numbers or
variables. The numerator of the fraction (m) represents the power, the
denominator (n) represents the root. The exponent in the denominator must
always be positive.
EXAMPLES A)
1
2
B)
x  x
1
2
9  9 3
𝑚
𝑎𝑛
C)
𝑛
= √𝑎𝑚
2
3
x  3 x2
PRACTICE: Write the expression in radical form:
7
A) x
B) a 4
2
5
PRACTICE: Write the expression in exponential form:
D) 3 c 5
C) 3 z 2
To simplify the square root of a number, create a factor tree and any two identical numbers may come out of
the radical. Buddy system! If there is no buddy, it must stay under the radical.
48
8
√18
√32
To simplify a cube root use the same process as a square root, except _________ of the same numbers are
needed to come out.
3
125
3
32 x 4 y 5
3
√54
The same is true for any other power outside the radical.
4
√625
4
√𝑥11
5
√64
EXAMPLES: Evaluate each exponential.
3
3/ 2
a. 25
c. 16
b. 27 2 / 3
3/ 2
d.
 64 
 64  2
e.  
 25 
2/3
If the radical contains variables:
• Divide power of variable by the root. The quotient is the new power of the variable outside the radical
• If there is a remainder, that is the power of the variable still under the radical.
A) x10
D) 5 243 x10 y 20
B) y 9
E ) 4 16 x8 y 9
F )  ( x  3)8
C ) 3 (4 x  7)24
EXAMPLES: Write all radicals as exponentials, and then apply the rules for rational exponents. Leave answers
in exponential form.
4
a)
5
x
3
x
b)
3 6
c)
x
3
32
2
EXAMPLES: Simplify – Write your answer in simplest root and exponential form.
a) (𝑥 3 𝑦 7 𝑧 8 )
1⁄
2
b) (8𝑥 5 )
5
1⁄
3 (2𝑥 ⁄3 )
c) (−125𝑥 4 √𝑥)
2⁄
3