Basic Mathematics for College Students

1.7 Prime Factors and Exponents 87

We can evaluate this exponential expression using the exponential key on

a scientific calculator on some models.

224

On a graphing calculator, we use the carat key to raise a number to a

power.

224

Since 224 16,777,216,there will be 16,777,216 bacteria after 24 hours.

¿ ENTER 16777216

¿

yx (^)  16777216
1 xy 2
yx

1. and 20 2. a. or b.Two possibilities are and
   3.1 and 23 4. a.no b.no 5. 6. 7. a.
   b. 52 (7^2 ) c. 23  32  5 8. a. 81 b. 216 c. 81 d. 12 9.1,350

1  2  9 2  3  3  7 2  2  3  3  3 32  7

1, 2, 4, 5, 10, 1 18, 2 9, 3  6 2  3  3

ANSWERS TO SELF CHECKS

SECTION 1.7 STUDY SET

VOCABULARY

Fill in the blanks.

1. Numbers that are multiplied together are called
   .


2. To a whole number means to express it as the
   product of other whole numbers.


3. A number is a whole number greater than 1
   that has only 1 and itself as factors.


4. Whole numbers greater than 1 that are not prime
   numbers are called numbers.


5. To prime factor a number means to write it as a
   product of only numbers.


6. An exponent is used to represent
   multiplication. It tells how many times the is
   used as a factor.


7. In the exponential expression the number 6 is the
   , and 4 is the.


8. We can read as “5 to the second power” or as “5
   .” We can read as “7 to the third power” or
   as “7 .”


9. Fill in the blanks to find the pairs of whole numbers
   whose product is 45.

The factors of 45, in order from least to greatest,

are: ,,,, ,

1   45 3   45 5   45

CONCEPTS

73

52

64 ,

10. Fill in the blanks to find the pairs of whole numbers
    whose product is 28.

The factors of 28, in order from least to greatest,

are: ,,,, ,

11. If 4 is a factor of a whole number, will 4 divide the
    number exactly?


12. Suppose a number is divisible by 10. Is 10 a factor of
    the number?


13. a. Fill in the blanks: If a whole number is divisible by
    2, it is an number. If it is not divisible by 2, it
    is an number.
    b. List the first 10 even whole numbers.

c. List the first 10 odd whole numbers.

14. a. List the first 10 prime numbers.

b. List the first 10 composite numbers.

15. Fill in the blanks to prime factor 150 using a factor
    tree.

The prime factorization of 150 is   .

150

30

5

3

1   28 2   28 4   28