Download Integer Exponents, Scientific Notation, and Order of Operations

Exponent Rules Assignment
Laws of exponents for real numbers a and b and integers m and n:
Rule
Example
Rule
Example
n
a  a =a
m
n
m+n
5  5 =5
2
am
= am – n
n
a
a0 = 1
a  bn
= a n  bn
a  = a
m n
Scientific Notation:
1.
mn
3  24  34  2 4
7 
3 2
 76
4
a
 a
  = n
b
b
a –n =
1
a
-n
1
a
–n = a
5 –3 =
n
 a
 b
  =  
b
a
n
4
2
16
 2
  = 4 =
3
3
81
n
–4
1
5
3 =
4
1
125
4
3
81
 2
 3
  =   = 4 =
3
2
2
16
1
 5 2  25
5 2
a  10 b , where 1 ≤ a < 10 and b is an integer
What power do each of the following figures represent? Also evaluate each expression.
(b)
Evaluate the following expressions. Show the exponent meaning in your work.
3
(a) 5
3.
6
89
 86
3
8
10 0 = 1
(a)
2.
4
n
(b) (-3)4
True or False. Explain your reasoning.
(c) 60
(d) 3 ∙ 52
(-2)4 = -24
___________
4
(e)  
5
2
Evaluate or simplify using the exponent rules. Show your step-by-step use of the rules!
4. 10  10  10
5
3
74
5. –4
7
6. 1.23456789
= 10
0
= _____
= 10
 3
7.  
 4
–2
4
= 
3
=7
= _____
or __________
or 5,764,801
Give a simplified fraction.
 
8. 4 3
2
4
9. 5 10 –5
= ________
10.
Give a simplified fraction.
4 3
5 2
11. 5 4  5 3  5 2
Give a simplified fraction.
.
Write in scientific notation:
12. $70 billion
= $70,000,000,000
13. 0.00016 cm
= _____ x 10
= _____ x 10
Write in standard decimal number notation.
14. $1.9 × 1013
16.
15. 8.45 × 10-7 seconds
Evaluate each expression for the given value of x. Show the substitution and each “order of operation”
step toward the solution.
x4
(a) 3x2 ; x = 5
(b) (3x)2 ; x = 4
(c)
; x -2
4
17.
Simplify. Use only positive exponents in your answers. Show correct use of the exponent rules.
(a) x ∙ x ∙ x
y12
(b) 4
y
 x 
(c)  
 10 
(d) (-4xy3)2
(e) (a4)-3
(f)
6
18.
3
24x 5 y 4 z
 3x 2 y 4 z 3
Evaluate.
 
(a)  3 2 3
2
19.
2
2
(b)  1   1
49
50
Now, be creative! Make up three problems involving exponents and exponent rules, and show your
work toward the solution.
(a)
(b)
(c)
Do your best! Rise to the challenge! Live and learn!