1. Integer Exponents
CA 2.0

2. Objective - To solve problems involving negative exponents and zero exponents.

3. Bases and Exponents x x ∙ x ∙ x = exponent base3 x
x ∙ x ∙ x =
base
The BASE tells us what is being multiplied.
The EXPONENT tells us how many times to multiply the base.

4. Identifying the Base & Exponent
The base is 5. The exponent is 2.
The base is 5. The exponent is 2.
The base is - 5. The exponent is 2.
The base is (x + 5). The exponent is 2.

5. Evaluating Exponents

6. Simple Rule Example: If the base is negative:
An even exponent means a positive answer
An odd exponent means a negative answer
Example:

7. For all real numbers x, x ≠ 0, and n is an integer:
Negative Exponents
For all real numbers x, x ≠ 0, and n is an integer:

8. Working with Negative Exponents
When you see a negative exponent, think FRACTION!
If no fraction exists, create a fraction, by putting what you have over 1!
Examples:

9. Fractions As Bases
If you have a fraction as the base, and there is a negative exponent:
FLIP THE FRACTION!
Example:

10. Simplify. 1) 3) 5) 2) 4) 6)

11. Follow the Pattern! = =
3 3 = 3 = 1 = = =

12. 3 3 3 3 1 Simplify. 1 Factor Explanation Negative Exponent Explanation2 -2
2 + -2 3 3 = 3 = 3 = 1 9 9 = 1
For all real numbers x, x ≠ 0,

13. Negative Exponents in Denominator
Evaluate.
Simplify. 1) 3) 2) 4)

14. Examples:

15. x x x 3 3 3 3 9 Negative exponents follow rules of exponents. = = = =
Rule of Common Bases a
a + b x x b x = 3 4
4 + -2 3 -2 3 3 2 9 = = = 81 81 = 9

16. ( ) ( ) ( ) x x 2 2 2 8 Negative exponents follow rules of exponents.
Power to Power Rule
( ) b a ab x x = -2
( ) 3
3(-2) -6 2 2 2 = = = = -2
( ) 8 = =

17. Simplify. 1) 4) 2) 5) 3) 6)

18. Simplify. 1) 4) 2) 5) 3) 6)