Presentation is loading. Please wait.

Presentation is loading. Please wait.

Properties of Exponents

Similar presentations


Presentation on theme: "Properties of Exponents"β€” Presentation transcript:

1 Properties of Exponents
August 27th, 2013

2 Exponential Expressions in Expanded Form
Write Each Expression in expanded form (4𝑦) 3 (4𝑦)(4𝑦)(4𝑦) βˆ’π‘Ž 2 -(a βˆ™ a) = -π‘Žβˆ™π‘Ž 2 𝑦 2 ( π‘₯βˆ’3) 3 2 𝑦 𝑦 π‘₯βˆ’3 π‘₯βˆ’3 (π‘₯βˆ’3) The base is 4y, and the exponent is 3. 4y is a factor 3 times.

3 Product of Powers Property
When multiplying two of the same bases, add the exponents. 4 2 βˆ™ 4 3 = 4 5 16 βˆ™ 64 = 1024 4 5 = 1024 π‘₯ 6 βˆ™ π‘₯ 2 = π‘₯ 8 (x βˆ™ x βˆ™ x βˆ™ x βˆ™ x βˆ™ x) βˆ™ (x βˆ™ x)

4 Power to a Power Property
When you have a power raided to another power, multiply the exponents. = 4 6 4 2 βˆ™ 4 2 βˆ™ 4 2 π‘₯ = π‘₯ 15 π‘₯ 3 βˆ™ π‘₯ 3 βˆ™ π‘₯ 3 βˆ™ π‘₯ 3 βˆ™ π‘₯ 3

5 Power of a Product Property
You can β€œdistribute” an exponent to other exponents. π‘₯ 2 𝑦 = π‘₯ 6 𝑦 4 5 π‘₯ 2 𝑦 = 25 π‘₯ 4 𝑦 6

6 Try these… π‘₯ 3 βˆ™ π‘₯ 8 π‘₯ 5 βˆ™π‘₯βˆ™ π‘₯ 2 𝑦 2 βˆ™ 𝑦 βˆ’8 βˆ™ 𝑦 11 𝑏 5 4 π‘Ž 7 0
𝑏 5 4 π‘Ž 7 0 6π‘₯ 𝑦 4 3

7 Multi-step Problems π‘Ž βˆ™ π‘Ž 5 3 4 π‘₯ βˆ™ 5π‘₯ 3 βˆ’2π‘₯ 3 βˆ™ π‘₯ 4 βˆ’2

8 Quotient of Powers Property
When dividing two of the same bases, subtract the exponents. 3βˆ™3βˆ™3βˆ™3βˆ™3 3βˆ™3 3 3 =27 π‘₯ 8 π‘₯ 3 π‘₯βˆ™π‘₯βˆ™π‘₯βˆ™π‘₯βˆ™π‘₯βˆ™π‘₯βˆ™π‘₯βˆ™π‘₯ π‘₯βˆ™π‘₯βˆ™π‘₯ π‘₯ 5

9 Power of a Quotient Property
You can β€œdistribute” an exponent to all the other exponents in a fraction. 9 16 π‘₯ 5 𝑦 π‘₯ 20 𝑦 12

10 Negative Power of a Quotient Property
If a fraction is raised to a negative exponent, flip the fraction and make the exponent positive. 2 5 βˆ’3 = π‘₯ 4 𝑦 7 βˆ’2 𝑦 7 π‘₯ 𝑦 14 π‘₯ 8

11 Try these… π‘₯ 8 π‘₯ 6 π‘₯ 7 π‘₯ 10 π‘₯ 5 π‘₯ 9 π‘₯ 4 𝑦 3 π‘₯ 5 𝑦 2 3 2 π‘₯ 4 𝑦 2 3
π‘₯ 8 π‘₯ 6 π‘₯ 7 π‘₯ 10 π‘₯ 5 π‘₯ 9 π‘₯ 4 𝑦 3 π‘₯ 5 𝑦 2 π‘₯ 4 𝑦 π‘₯ 2 𝑦 6 βˆ’5


Download ppt "Properties of Exponents"

Similar presentations


Ads by Google