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

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?

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 86 = 8 x 8 x 8 x 8 x 8 x 8 84 x 82 83 x 83 Notice the pattern in the exponents!! The sums 4 + 2 and 3 + 3 both equal 6, the exponent of 8.

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

Multiplying Powers in an Algebraic Expression Simplify each expression.

More Practice

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

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

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)

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.)

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.

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

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

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

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

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

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