1. Good Day Have homework out to be checked!!
Put questions on the board!!
Complete the day 3 warm-up
Warm-up Quiz on Friday!!

2. 7–3 & 7-4 Multiplication Properties of Exponents
8.3 & 8.4
7–3 & 7-4 Multiplication Properties of Exponents
Essential Question: How can the rules for multiplying and dividing monomials be determined using other properties?

3. Multiplying Powers Notice the pattern in the exponents!!
You can write a power as a product of powers with the same base. Think of the power as the product of two factors.
86 = 8 x 8 x 8 x 8 x 8 x = 8 x 8 x 8 x 8 x 8 x 8
x x 83
Notice the pattern in the exponents!!
The sums and both equal 6, the exponent of 8.

4. Property: Multiplying Powers with the Same Base
For every nonzero number a and integers m and n, am x an = am+n
Examples:

5. Multiplying Powers in an Algebraic Expression
Simplify
each
expression.

6. More Practice

7. Good Day!! Have homework out to be checked Put questions on the board
Complete the day 4 warm-up
Get your thinking caps on!!

8. Put on your thinking caps!!
Simplify each expression.
2x(3y) =
3x3(2y2) =
4x3(2y2)(2z) =
-2y2(3y2z)(4z3) =

9. Multiplying Numbers in Scientific Notation
Simplify (7 x 102)(4 x 105). Write the answer in scientific notation.
Now try this one: (2.5 x 108)(6 x 103)

10. Good Morning Have homework out to be checked!!
Prepare for warm-up quiz (sharpen pencils BEFORE the bell rings)
No Talking – Eyes on your own paper (10 min.)

11. Investigation!!!
You can use what you learned in the last lesson to find a shortcut for simplifying expressions with powers. Complete each statement.
5.) Make a conjecture! What pattern do you see in your answers?
6.) Use your pattern to simplify (86)3.

12. Property: Raising a Power to a Power
For every nonzero number a and whole numbers m and n, (am)n = amn
Examples:
Now you try it!
1.) Simplify (x3)6
2.) Simplify (a4)7 and (a-4)7

13. Simplify Now try this one:
Example 2 – Simplifying an expression with Powers
Simplify
Now try this one:

14. Raising a Product to a Power
You can use repeated multiplication to simplify expressions like (5y)3. Notice that (5y)3 = 53 y3 This is another property of exponents! Property: Raising a Product to a Power For every nonzero number a and b and whole number n, (ab)n = anbn. Example: (3x)4 = 34x4 = 81x4

15. Example 3 – Simplifying a product raised to a power.
Now try these:

16. Example 4 – Simplifying a product raised to a power.
Now try these:

17. Tonight’s Assignment
Complete the 7-3 Homework assignment on your unit outline
Study for a quiz on 7-1 to 7-3