The document provides an overview of exponent rules, including the product, quotient, and power rules, as well as how to simplify exponential expressions. It explains scientific notation as a method for expressing very small and large numbers using exponents of 10, detailing the process for converting numbers to and from standard notation. Examples are included to illustrate both the simplification of exponents and the application of scientific notation.

1. 1.2 Exponents and Scientific
Notation
Chapter 1 Prerequisites

2. Concepts & Objectives
⚫ Objectives for this section:
⚫ Use exponent rules.
⚫ Find the power of a product and a quotient.
⚫ Simplify exponential expressions.
⚫ Use scientific notation.

3. Properties of Exponents
⚫ Recall that for variables x and y and integers a and b:
Product Rule
Quotient Rule
Power Rule
Zero Exponent
Negative Rule
+
=
a b a b
x x x
−
=
a
a b
b
x
x
x
( ) =
b
a ab
x x
−
=
1
a
a
x
x
=
0
1
x

4. Simplifying Exponents
⚫ Example: Simplify
⚫ 1.
⚫ 2.
⚫ 3.
−
3 2 2
2 5
25
5
x y z
xy z
( )
−
4
2 3
2r s t
( )
4
2 5
3x y
−
−

5. Simplifying Exponents
⚫ Example: Simplify
⚫ 1.
⚫ 2.
⚫ 3.
−
3 2 2
2 5
25
5
x y z
xy z
( )
−
4
2 3
2r s t
( )
4
2 5
3x y
−
−
3 1 2 2 2 5
25
5
x y z
− − − −
=
( ) ( ) ( )
4 2 4 3 4 1
4
2 r s t
−
=
( ) ( ) ( )
4 2 4 5 4
3 x y
−
= −
− −
= 2 4 3
5x y z
−
= 8 12 4
16r s t
8 20
81x y
−
=

6. Scientific Notation
⚫ A shorthand method of writing very small and very large
numbers is called scientific notation, in which we express
numbers in terms of exponents of 10.
⚫ To write a number in scientific notation
⚫ Move the decimal point to the right of the first nonzero digit in
the number.
⚫ Write the digits as a decimal number between 1 and 10.
⚫ Count the number of places n that you moved the decimal point.
⚫ Multiply the decimal number by 10 raised to a power of n. If you
moved the decimal left (large number), n is positive; if you
moved it right (small number), n is negative.

7. Scientific Notation (cont.)
Example: Write 2,780,000 in scientific notation.

8. Scientific Notation (cont.)
Example: Write 2,780,000 in scientific notation.
⚫ Moving the decimal 6 places to the left means n = 6,
therefore our answer is
⚫ Notice that we can drop the extra zeros.
6 places to
the left
 6
2.78 10

9. Scientific Notation (cont.)
Example: Write 0.00000000000047 in scientific notation.

10. Scientific Notation (cont.)
Example: Write 0.00000000000047 in scientific notation.
⚫ Moving the decimal 13 places to the right means n = ‒13,
therefore our answer is
13 places
to the left
13
4.7 10−


11. Scientific Notation (cont.)
⚫ To convert a number in scientific notation to standard
notation, simply reverse the process.
⚫ Move the decimal n places to the right if n is positive
or n places to the left if n is negative.
⚫ Add zeros as needed.
⚫ Remember, if n is positive, the absolute value of the
number is greater than 1, and if n is negative, the
absolute value of the number is less than 1.

12. Scientific Notation (cont.)
Example: Convert 3.547×1014 to standard notation.
Shift the decimal point 14 places to the right and fill
in the blanks with 0s.
354700000000000 or 354,700,000,000,000

13. Scientific Notation (cont.)
Example: Convert 7.91×10‒7 to standard notation.
Shift the decimal point 7 places to the left and fill in
the blanks with 0s.
.000000791 or 0.000000791

14. Classwork
College Algebra 2e (OpenStax.org)
⚫ 1.2: 6-24 (even); 1.1: 28-56 (×4)
⚫ 1.2 Classwork Check (in Canvas)
⚫ Quiz 1.1