1 / 10

Exponents and Equivalent Forms: Zero and Negative Exponents

Learn about zero and negative exponents and their properties, including how to convert negative exponents to positive exponents and simplify exponential expressions. Also, explore real-world problem-solving involving population growth.

gober
Download Presentation

Exponents and Equivalent Forms: Zero and Negative Exponents

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Section 8-1: Zero and Negative Exponents Objectives: (1) To understand that numbers in the real number system are represented in a variety of equivalent forms (2) To add, subtract, multiply and divide exponential expressions

  2. Properties • Zero Exponent Property • For every nonzero number a, a0 = 1 • Examples • 50 = 1 (-2)0 = 1 (-1.02)0 = 1 (1/2)0 = 1 • Negative Exponent Property • For every nonzero number a and integer n, a-n= • Examples • 6-4 = (-8)-1 =

  3. Converting Negative Exponents to Positive Exponents • Step 1: Make every number with a negative exponent a fraction (easiest way to convert any number into a fraction is putting it over 1) • Step 2: Move the number to the other side of the fraction bar and change the sign • Step 3: If there are no numbers left on one side of the fraction bar, put a 1 to represent that there was a number there originally.

  4. Examples of Converting Negative Exponents • 4-3 • 1 _ 43 • 1 _____ 4 • 4 • 4 • 1__ This is what we call 64 simplifying a power

  5. Simplifying an Exponential Expression Simplify the expression 4yx-3 4y X3 • Use the definition of negative exponents • Simplify • We’re done! • Tada!

  6. Simplifying an Exponential Expression Simplify the expression: 1 w-4 w4 • Move the w to the other side of the fraction bar • You’re done! • Tada!

  7. Evaluating Exponential Expressions Evaulate: 3m2t-2 for t = -3, m = 2 3m2 t2 3(2)2 (-3)2 3(4) 9 12 9 4 3 • 1st: Convert to positive exponents • 2nd: Plug in values (put them in parenthesis) • 3rd : Simplify • You’re done

  8. Real-World Problem Solving • Population Growth: A biologist is studying green peach aphids (a bug). In the lab, the population doubles every week. The expression 1000 • 2wmodels an initial population of 1000 insects after w weeks of growth. • Evaluate the expression for w = 0. Then describe what the value of the expression represents in the situation. • Evaluate the expression for w = -3. Then describe what the value of the expression represents in the situation.

  9. Part A 1000 • 2w 1000 • 20 1000 • 1 1000 • Plug in 0 for w • Now evaluate • What does 1000 represent? • The initial number of aphids

  10. Part B 1000 • 2w 1000 • 2-3 1000 • 1000 • 125 • Plug in -3 for w • Now evaluate • What does 125 represent? • The number of aphids 3 weeks ago

More Related