Exponent Properties involving ProductsExponent Properties involving Products

Algebra 1 HonorsAlgebra 1 Honors8.18.1

Day 1Day 1

Warm UpWarm UpRead the sheet. Read the sheet. 1. Underline any words you don’t know or 1. Underline any words you don’t know or

understand and write them on your Warm Up.understand and write them on your Warm Up.2. Write one or two sentences that summarize 2. Write one or two sentences that summarize

the reading.the reading.3. Write a sentence about one new fact you did 3. Write a sentence about one new fact you did

not know before.not know before.4. Find 64. Find 67 7 using a calculatorusing a calculator

Notes:Notes:

Notice what happens when you Notice what happens when you multiple two powers that have multiple two powers that have the same base:the same base:

aa22 x a x a3 3

Notes:Notes:

Product of Powers Property:Product of Powers Property:Let Let aa be a real number, and let be a real number, and let mm and and nn be be

positive integers. positive integers. To multiply powers having the same base, To multiply powers having the same base,

add the exponents.add the exponents.aamm x a x ann = a = am + nm + n

Ex. 5Ex. 566 x 5 x 533 = =

Use the product of powers Use the product of powers property:property:

7733 x 7 x 755 = =

9 x 99 x 988 x 9 x 92 2 ==

(-5)(-5)(-5)(-5)6 6 ==

(x(x44)(x)(x33) = ) =

Notes:Notes:

Power of a Power: Power of a Power: Notice what happens when you raise a Notice what happens when you raise a power to a power:power to a power:

(a(a22))3 3 ==

Notes:Notes:

Let Let aa be a real number, and let be a real number, and let mm and and nn be be positive integers. positive integers.

To find a power of a power, multiply To find a power of a power, multiply exponents.exponents.

(a(amm))nn = a = amnmn

Ex. (3Ex. (344))22

REMEMBER!REMEMBER!

Use the power of a power Use the power of a power property:property:

(2(255))33 = = (-6(-622))5 5 ==

(x(x22))44== ((y+2)((y+2)66))22 = =

Notes:Notes:

Notice what happens when you raise a product Notice what happens when you raise a product to a power.to a power.

(ab)(ab)33 = =

Notes:Notes:

Let Let aa and and bb be real numbers, and let be real numbers, and let mm be a be a positive integer.positive integer.

To find a power of a product, find the power of To find a power of a product, find the power of each factor and multiply.each factor and multiply.

((ab)ab)mm= a= ammbbmm

Ex. (23 x 17 )Ex. (23 x 17 )5 5 = 23= 2355 x 17 x 1755

Use the power of a product Use the power of a product property:property:

(24 x 13)(24 x 13)88

(9xy)(9xy)22

(-4z)(-4z)22 -(4z)-(4z)22

Use all three:Use all three:

(2x(2x33))22 (x (x44))

White boardsWhite boards

PracticePractice

3322 x 3 x 377

PracticePractice

(x(x22 )(x )(x77))

PracticePractice

(5(522)(4)(433))

PracticePractice

(-7)(-7)22 (-7) (-7)

PracticePractice

5 x 55 x 599

PracticePractice

(4(422))77

PracticePractice

(n(n33))66

PracticePractice

((m+1)((m+1)44))55

PracticePractice

(42 x 12)(42 x 12)22

PracticePractice

(-3n(-3n33))22

PracticePractice

(9mn(9mn22))44 (m) (m)

Homework:Homework:

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

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