1. G OOD D AY !! Have homework out to be checked Complete Day 4 No Talking – Remember you are competing for a 100 quiz grade!! Warm-up Quiz Tomorrow!!

2. T URN UP THE VOLUME !! The volume of a cube can be found by cubing one of its sides What does it mean to cube a side? In other words, Volume formula: V = e 3. Find an expression for the volume of the storage bin shown which is 3y 2 on each side. V = You Try these: Find the volume of a cube where each edge is:1) 4x 5 2) 3a -2

3. 7-5 D IVISION P ROPERTIES OF E XPONENTS Objective: To discover division properties of exponents and to use these properties to simplify exponential expressions involving quotients Why? To determine the volume remaining after a cubed shaped box is filled halfway, you can use division properties of exponents

4. L ET ’ S SEE W HAT YOU KNOW ? You can use repeated multiplication to simplify fractions. Expand the numerator and the denominator using repeated multiplication, then cancel like terms.

5. I NVESTIGATION OF Q UOTIENTS (7 MIN. – 3 NO TALKING 2 DISCUSS WITH A NEIGHBOR 2 MIN - SHARE Expand each power and simplify x 7 = ______________________ x 3 How can you simplify exponents when you divide like bases? Duplicate the quotient by the specified power How many x’s (not x 2 ) do you have now? y’s? What happens to each base inside the parenthesis when you raise a quotient to a power?

6. P ROPERTY : D IVIDING P OWERS WITH THE S AME B ASE For every nonzero number a and integers m and n, a m = a m-n a n Examples:

7. S IMPLIFYING AN A LGEBRAIC E XPRESSION Simplify each expression.

8. R AISING A Q UOTIENT TO A P OWER You can use repeated multiplication to simplify this expression: Property: Dividing Powers with the Same Base For every nonzero number a and b and integer n, Example:

9. H OW ARE THESE ALIKE ? H OW ARE THEY DIFFERENT ? Property: Raising a Product to a Power For every nonzero number a and b and whole number n, (ab) n = a n b n. Property: Raising a Quotient to a Power For every nonzero number a and b and integer n,

10. GOOD DAY! Prepare for warm-up quiz Sharpen pencils, Be seated, and STOP TALKING!! Have homework out to be checked Put questions on the board!!

11. Example – Raising a Quotient to a Power Simplify Now try these:

12. Example – Raising a Quotient to a Negative Power Simplify Now try these:

13. L ET ’ S R ACE TO THE T OP Remember you are dividing like bases today!! Be careful on your subtraction rules – use KCC!!

14. C REATE YOUR OWN PROBLEM Try to create a problem which would fit each description below: 1) Has more x’s in the denominator than the numerator 2) When raised to a power you get an even number of x’s but an odd number of y’s

15. E XIT T ICKET Explain how you would simplify the following expression. Use complete sentences & specific details.