1. The Laws of Exponents

2. Exponents
exponent
Power
base
53 means 3 factors of 5 or 5 x 5 x 5

3. #1: Exponential form: The exponent of a power indicates
The Laws of Exponents:
#1: Exponential form: The exponent of a power indicates
how many times the base multiplies itself.
n factors of x

4. #2: Multiplying Powers: If you are multiplying Powers with the same base, KEEP the BASE & ADD the EXPONENTS!
So, I get it! When you multiply Powers, you add the exponents!

5. Exponent patterns Rule: na•nb = na+b Multiplication Rule
What rule can you identify from the following examples?
52•53= _____ =55
34 •32 = ____ =36
28 •26= ____ =214
Rule: na•nb = na+b
Multiplication Rule
When you multiply two powers that have the same base, add the exponents and keep the base

6. Why does the multiplication rule work?
na•nb = na+b
52 • 53
(5•5) • (5•5•5)
5•5•5•5•5 55

7. Simplify using exponents:
72•73
95 •93
36 •3-1
= ____ = ___
= ____ = ___
= ____ = ___

8. #3: Dividing Powers: When dividing Powers with the same base, KEEP the BASE & SUBTRACT the EXPONENTS!
So, I get it!
When you divide Powers, you subtract the exponents!

9. Exponent patterns Rule: na  nb = na-b Division Rule
What rule can you identify from the following examples?
5451 = _____ =53
89  82 = _____ =87 66 62
Rule: na  nb = na-b
= _____ =64
Division Rule
When you divide two powers that have the same base, subtract the exponents and keep the base

10. Why does this rule work?
na  nb = na-b 35 32
3•3•3•3•3
3•3 33

11. Simplify using exponents:
78÷73
95 ÷91
69 ÷6-5
= ____ =___
= ____ =___
= ____ = ___

12. Try these:

13. SOLUTIONS

14. SOLUTIONS

15. #4: Power of a Power: If you are raising a Power to an exponent, you multiply the exponents!
So, when I take a Power to a power, I multiply the exponents

16. Exponent patterns Rule: (na )b = na*b Power Rule
What rule can you identify from the following examples?
(54)1 = _____ =54
(89)2 = _____ =818
(32)5 = _____ =310
Rule: (na )b = na*b
Power Rule
When you take the power of a power, multiply the exponents and keep the base

17. (52 ) 3 52•52•52 52+2+2 56 Why does this rule work?
Rule: (na )b = na*b
(52 ) 3
52•52•52
52+2+2 56

18. Simplify using exponents:
(142 ) 5
(84 ) 11
(6-5 ) -4
= ____ = ___
= ____ =___
= ____ = ___

19. #5: Negative Law of Exponents: If the base is powered
by the negative exponent, then the base becomes reciprocal with the
positive exponent.
So, when I have a Negative Exponent, I switch the base to its reciprocal with a Positive Exponent.
Ha Ha!
If the base with the negative exponent is in the denominator, it moves to the numerator to lose its negative sign!

20. #6: Zero Law of Exponents: Any base powered by zero exponent equals one.
So zero factors of a base equals 1. That makes sense! Every power has a coefficient of 1.

21. Try these:

22. SOLUTIONS

23. SOLUTIONS

24. #7: Product Law of Exponents: If the product of the bases is powered by the same exponent, then the result is a multiplication of individual factors of the product, each powered by the given exponent.
So, when I take a Power of a Product, I apply the exponent to all factors of the product.

25. #8: Quotient Law of Exponents: If the quotient of the
bases is powered by the same exponent, then the result is both
numerator and denominator , each powered by the given exponent.
So, when I take a Power of a Quotient, I apply the exponent to all parts of the quotient.

26. Try these:

27. SOLUTIONS

28. SOLUTIONS