Exponent Properties involving Products Algebra 1 Honors 8.1 Day 1

Warm Up Read the sheet. 1. Underline any words you don’t know or understand and write them on your Warm Up. 2. Write one or two sentences that summarize the reading. 3. Write a sentence about one new fact you did not know before. 4. Find 6 7 using a calculator

Notes: Notice what happens when you multiple two powers that have the same base: a 2 x a 3

Notes: Product of Powers Property: Let a be a real number, and let m and n be positive integers. To multiply powers having the same base, add the exponents. a m x a n = a m + n Ex. 5 6 x 5 3 =

Use the product of powers property: 7 3 x 7 5 = 9 x 9 8 x 9 2 = (-5)(-5) 6 = (x 4 )(x 3 ) =

Notes: Power of a Power: Notice what happens when you raise a power to a power: (a 2 ) 3 =

Notes: Let a be a real number, and let m and n be positive integers. To find a power of a power, multiply exponents. (a m ) n = a mn Ex. (3 4 ) 2

REMEMBER!

Use the power of a power property: (2 5 ) 3 =(-6 2 ) 5 = (x 2 ) 4 =((y+2) 6 ) 2 =

Notes: Notice what happens when you raise a product to a power. (ab) 3 =

Notes: Let a and b be real numbers, and let m be a positive integer. To find a power of a product, find the power of each factor and multiply. (ab) m = a m b m Ex. (23 x 17 ) 5 = 23 5 x 17 5

Use the power of a product property: (24 x 13) 8 (9xy) 2 (-4z) 2 -(4z) 2

Use all three: (2x 3 ) 2 (x 4 )

White boards

Practice 3 2 x 3 7

Practice (x 2 )(x 7 )

Practice (5 2 )(4 3 )

Practice (-7) 2 (-7)

Practice 5 x 5 9

Practice (4 2 ) 7

Practice (n 3 ) 6

Practice ((m+1) 4 ) 5

Practice (42 x 12) 2

Practice (-3n 3 ) 2

Practice (9mn 2 ) 4 (m)

Homework: Pg. 492/ 3-6, 11-14, 31

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