Exponents
Higher Exponents
Zero Exponent
Number Properties
100
Simplify 
.
100
(a)Compute 
.
(b)For how many integers 
is 
between 
and 
?
(a) -64
(b) 7
100
Consider the exponent facts below:
(a)In these equations, what pattern do you see in the numbers on the right?
(b)Assuming that your pattern continues, predict the value of 
.
(a)Each number on the right is the number above it divided by 2. For instance, 16 divided by 2 is 8, and 8 divided by 2 is 4.
(b)According to the pattern, the missing number should be 2 divided by 2, which is 1. So we predict 
is 1.
100
How many prime numbers are there between 5 and 24 inclusive?
7
200
What is the value of 
when 
?
200
Let 
be any number.
(a)Explain why 
.
(b)Explain why 
.
(a) a^4
(b) -a^5
200
Evaluate 
.
43
200
If 3 * (S+T) = 24 and S is a prime number, then what could be T?
A) 8
B) 7
C) 4
D) 3
D
300
1. Evaluate 
.
2. How are 
and 
related?
1. 
.
300
Evaluate 
.
300
Let be any number. Simplify 
.
4
300
What is the sum of the distinct prime factors of 24?
5
400
(a)What is 
?
(b)The expression 
is the negation of the square of 2. What number does equal?
(c)Given 
, find the value of 
.
(a)
(b)
(c)
6
400
Addition and multiplication are commutative. That is, 
and 
for all and 
. In this problem, we explore whether or not exponentiation is commutative.
(a)What is 
?
(b)What is 
?
(c)Is exponentiation commutative? That is, if and are positive integers, then must we have 
?
(a)
(b)
.
(c)In parts (a) and (b), we found that 
and 
are not equal. Therefore, we know that exponentiation is not commutative. The order of the numbers in a power matters.
400
Let 
and 
. What is the value of
1
400
The sum of 4 consecutive integers is 122. What is the largest of the four integers?
32
500
(a)What is the value of 
?
(b)What is the value of 
?
(c)Is equal to ?
(a)The value of 
is 
(b)The value of 
is 
(c)No. By the first two parts, is greater than , so the two expressions are not equal.
500
Addition and multiplication are associative. That is, 
and 
for any numbers , , and 
. In this problem, we explore whether or not exponentiation is associative.
(a)What is 
?
(b)What is 
?
(c)Is exponentiation associative? That is, if , , and are positive integers, must we have 
?
(a)We evaluate inside the parentheses first:
(b)Again, we evaluate inside the parentheses first:
(c)We just showed that 
is different from 
. So exponentiation is not associative; where we place parentheses in expressions like 
and matters.
500
Let 
be a number. Evaluate 
.
3
500
The product of three consecutive integers is 210. If one of the integers is 6, what is the sum of the three integers?
18