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. Evaluate each expression.
(5z)-3 (-6)0 -m – 2-1

13. The Quotient Rule
Quotient Rule for Exponents

14. Applying the Quotient Rule
Simplify each quotient.

15. Simplify each quotient.

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

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

18. 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.

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

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

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

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

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

24. Evaluate the following by using scientific notation.