1. 7.5 Properties of Exponents and Scientific Notation

2. Exponents and Exponential Expressions
Exponents are used to write products of repeated factors.
Ex. 3 • 3 • 3 • 3 = 34
In the above example, the 4 is the exponent and 3 is the base.
The quantity 34 is called an exponential expression.

3. Evaluating Exponential Expressions
Evaluate each exponential expression. 72
-42
(-2)4

4.  Evaluate each exponential expressions.
(-2)5 -24

5. The Product Rule Product Rule for Exponents: am • an = am + n
Apply the product rule for exponents in each case.
34 • 37
(5y2)(-3y4)

6. Apply the product rule for exponents in each case.
53 • 5 y3 • y8 • y2 (7p3q)(2p5q2)

7. The Power Rules
Power Rules for Exponents

8. Applying the Power Rules
Simplify each expression.
(p8) (3y)4

9.  Simplify each expression.

10. Zero and Negative Exponents
Zero Exponent a0 = 1 Negative Exponent Special Rules for Negative Exponents

11. Evaluating Exponential Expressions
Evaluate each expression. z
(-m)-4 (8k)

12. The Quotient Rule
Quotient Rule for Exponents

13. Applying the Quotient Rule
Simplify each quotient.

14. Writing Expressions with No Negative Exponents
Simplify each expression so that no negative exponents appear in the final result.
32 • (x-4)6

15. Simplify each expression so that no negative exponents appear in the final result.
x-3 • x-4 • x2 (4-2)-5 (23x-2)-2

16. Scientific Notation
Many of the numbers that occur in science are very large or very small.
Writing these numbers is simplified by using scientific notation.
Scientific Notation
A number is written in scientific notation when it is expressed in the form a x 10n, where 1 ≤ |a|< 10 and n is an integer.

17. IB Exam Information (NOT in your book!)
Express your answer in the form a x 10k, where 1 ≤ |a|< 10 and k Є .
FYI:
Є means “is an element of”
represents “all integers”

18. Converting to Scientific Notation
Convert each number from standard notation to scientific notation.
8,200,000

19. Convert each number from standard notation to scientific notation.
46,

20. Converting from Scientific Notation
Convert each number from scientific notation to standard notation.
6.93 x 105
4.7 x 10-6

21. Convert each number from scientific notation to standard notation.
2.317 x x 10-4

22. Using Scientific Notation in Computation
Evaluate by using scientific
notation.

23. Evaluate the following by using scientific notation.