Warm Ups

• -7 • c • c • c • y • y =

• Is 45 divisible by 3?

• When solving a problem with exponents and grouping symbols, which do you do first?

• What is a composite number?

• What strategy do we use to find prime factors of a number?

Section 4.7: Exponents and MultiplicationThe Exponential Jungle.October 16th NotesNeed your thinking caps today so stay with me.

Multiplying Exponents: You Figure It Out

72 73 =

54 52 =

b7 b1 =

Hint: Expand the exponents.

Multiplying Exponents

• To multiply numbers OR variables with the same base, add the exponents.

• Arithmetic: 23 24 = 23+4 = 27

2 2 2 2 2 2 2 = 27

• Algebra: pm pn = pm+n = pm+n

So SIMPLIFY! 3 33 =

a5 a b2 =

x2 x3 y y4 =

-2x2 3x5 =

4x2 3x4 =

Finding a Power of a Power

• (72)3 =

• Rule for Multiplying Powers with the Same Base.

• Raise a power to a power by multiplying the exponents.

• (72)3 = (72) (72) (72) = 72+2+2 = 76

• OR! (72)3 = 72 3 = 76

• Remember your Order of Operations. Get stuff done inside the PARENTHESES first, then the EXPONENTS!

Simplify each expression.

• (24)2 =

• (c5)4 =

• (m3)2 =

Section 4.8: Exponents and DivisionThe Exponential Jungle.

October 16th Notes

Dividing Powers with the Same Base.

• 78/73 =

• 116/115 =

Dividing Powers with the Same Base.

• To divide numbers or variables with the same nonzero base, you subtract exponents.

• Arithmetic: 45/42 = 45-2 = 43

• Algebra: am/an = am-n

• Try these:

• 12m5/3m =

• 200m200/100m100 =

Simplifying Expressions with Integer Exponents

• What happens when you divide powers with the same base and get zero as the exponent? Like this…write with a fraction bar.

• 34/34 =

• 34/34 = 34-4 = 0 = 30

• ZERO AS AN EXPONENT Rule:

• 30 = 1

• a0 = 1, when a 0

Try These:

• (-8)2/(-8)2 =

• 6b3/18b3 =

 

• 5x0 =

• 52x6/5x6 =

But..what about NEGATIVES and EXPONENTS!?!?

• What if you divide and you get a negative exponent? Write in expanded form with fraction bar.

• 32/34 =

• 32/34 = 32-4 = -2 = 3-2

• 32/34 = 1/32

Negative Exponents

• Arithmetic: 3-2 = 1/32

• Algebra: a-n = 1/an

• If you forget why these rules are true, always write the example in an expanded form. That will remind you why these rules are true.

Need to Re-Write an Expression?

• When simplifying an expression with a negative exponent, you can write it as a fraction with a positive exponent:

4-2 = 1/42 = 1/16

• You can also write an expression with a fraction so that there is no fraction bar:

1/x2 = x-2

Example Problems: Simplify as much as you can…

• 56/58 =

• 45/47 =

• a4/a6 =

• 3y8/9y12 =

Write without a Fraction Bar:

• x2y3/x3y =

• b3/b9 =

• m3n2/m6n8 =

• dr5/d5r3 =

Assignment #25• Page 200: 11-27 odd.

• Page 206: 17-39 odd.

• START YOUR HOMEWORK NOW…

• If there is time…

• I highly recommend that you keep your notes open while you do your homework. That way you can look at your notes to remind yourself what to do when.

• If all else fails, ORDER OF OPERATIONS!