7.1 – Exponent Properties 1
Write your questions
and thoughts here!
Recall: Exponent Rules…
"Product
Rule!"
"Quotient
Rule!"
Power of a
Power
Power of a
Product
Power of
Quotient
"Negative
Exponent
Rule"
Quotient of
Powers
Negative
Exponents
"Zero
Exponent
Rule"
Product of
Powers
"Power Rule!"
Property Name Zero
Exponents
What this means: Algebra I
Section 9.1 – 9.3
Example Examples: Simplify. Use only positive exponents. What rule did you use? 1.
4! ∙ 4!!
4.
!
7. −2𝑥
!"! ! ! ! !
!! !!
2.
5.
−3!
− 1𝑥
3.
!
8. 6𝑔! ∙ 4𝑔!
6. 9.
−3
!
!
!
!!
5𝑥𝑦 !! 𝑧 !
!
7.1 – Exponent Properties 2
10. 13. !! !
! ! ! ! !
11. 4𝑥 𝑦 𝑥 𝑦
!"! !!
!"! !! ! !!
14. !! !! !
GRAPH
Below, the graph of 𝑓 𝑥 = 𝑥 + 1 − 2 is
sketched in bold. Its parent function
3.
𝑓 𝑥 = 𝑥 is represented by the thin curve.
!! !! ! !
!! ! ! !
Algebra Skillz
SIMPLIFY
98 + 18
!
12. 15.
SOLVE
5. Solve:
𝑥 − 1 2𝑥 + 7 = 0
2. How does the translation relate to the
equation?
6. Factor and solve.
𝑥 ! − 12𝑥 + 35 = 0
!
!! !!
!!
!
!" !"# !"
!!! ! ! ! !!
1. Describe the translation of the parent
graph.
4. −2 8 + 15
!"! !
! !

7.1 Exponent Rulez
Practice
Simplify completely. Use only positive exponents.
1) (  )

3) ( y  )
5)
7)
9)


2) ( x  )

4) (uv  )

6)

x
8)
x
y


n
n 
10)    
x y
11)    
12) n  n 
13)  x y   y x 
14) () 
15) ( x  )

16) (n  )
-1-

Worksheet by Kuta Software LLC

17) ( x  y  )
19)

18)
 
20)  


21)  
23)

22)
m 
24)
m 
25) v 
r 
r 
x y
x y
26) b 
Simplify completely. Use only positive exponents. BRING THE PAIN!
27)
29)
(  ) 
m  n 
(( ) )
n
31)
33)
28)
   
(
 

30)
 
m n
m  n  m  n 
(m  n  ) 
yx
( x  y  )  x 
)

32)
34)
-2-
 
( )


( y x  ) 
 x  y   y 
( x  y )  y 
x y
m  n  n 
(nm ) 
Worksheet by Kuta Software LLC
Ap p l i c a t
ion
7.1 – Exponent Properties 3
Simplify. Use only positive exponents. 1.
2𝑥 ! ∙ 3𝑥 !
−7!
2.
3. !"! ! ! !
!"! !! ! !
4. Write an expression for the figure's area or volume in terms of x.
a.
𝐴=
! !
𝑠 !
b.
𝑉 = 𝜋𝑟 ! ℎ
c.
𝑉 = 𝑙𝑤ℎ
𝑥
𝑥
3
𝑥
2
𝑥
2𝑥
5.
5𝑥
3
Solve each equation for x by finding a common base:
a.
3!
!
= 3!
Hint: rewrite 2048 as 2
Hint: rewrite 9 as 32
b.
9!! = 3!"
c.
22x + 1 = 2048
?
d.
!
5! = 25 !!!!"
SAT Review
MUTIPLE CHOICE
If 14!!" = 14
(A)
(B)
(C)
(D)
(E)
!!
, then the value of k =
Cannot be determined
14
−14
7
−7
DOUBLE MULITPLE CHOICE ?!?!?!
If 0 < a < 1, which of the following gives the
correct ordering of 𝑎, 𝑎, and 𝑎! ?
(A) 𝑎 < 𝑎 < 𝑎!
(B) 𝑎 < 𝑎! < 𝑎
(C) 𝑎 < 𝑎 < 𝑎!
(D) 𝑎 < 𝑎! < 𝑎
(E) 𝑎! < 𝑎 < 𝑎