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Understanding Monomials, Powers, and Scientific Notation Exercises

This warm-up exercise aims to simplify various algebraic expressions, focusing on the concept of monomials, coefficients, and degrees. A monomial is defined as a product of numbers and variables without addition or subtraction, negative exponents, or roots. The session will also cover scientific notation for expressing large and small numbers and dimensional analysis using unit conversions. Students will engage with example problems and hands-on practice to reinforce their understanding of these essential mathematical concepts.

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Understanding Monomials, Powers, and Scientific Notation Exercises

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Presentation Transcript

  1. Warm-Up: October 31, 2011 • Simplify the following expressions

  2. Monomials Section 5-1

  3. Monomial • A monomial is an expression that is a number, a variable, or the product of a number and one or more variables. • Cannot contain: • Addition or subtraction • Variables in denominators • Negative exponents of variables • Fractional exponents of variables • Roots of variables (square root, cube root, etc.)

  4. Definitions • Constants are monomials without variables • 5, -7, 13 • A coefficient is the numerical factor of a monomial. • 3 is coefficient of x2 in 3x2 • -5 is the coefficient of xy in -5xy • The degree of a monomial is the sum of the exponents of its variables. • 5x3 has degree 3 • -2xy has degree 2 • Any constant has degree 0

  5. Power • A power is an expression of the form xn, or simply the exponent n. • Physics: Work overtime to get power.

  6. Simplify • In order for an expression to be simplified, the following must be true: • No parentheses • No negative exponents • All fractions simplified • No square roots in the denominator • No negative sign in the denominator

  7. Negative Exponents • Negative exponents move quantities to the other side of a fraction bar

  8. Product Rule

  9. Example 1 - Simplify

  10. You-Try #1 - Simplify

  11. Quotient Rule

  12. Example 2 – Simplify

  13. You-Try #2 – Simplify

  14. Properties of Powers

  15. Example 3 – Simplify

  16. You-Try #3 – Simplify

  17. Example 4 – Simplify

  18. You-Try #4 – Simplify

  19. Warm-Up: November 1, 2011 • Simplify

  20. Scientific Notation • Scientific notation is used to express very small or very large numbers • 1 ≤ a < 10 • n is an integer, and is the number of places to move the decimal point • If the number in standard notation is greater than 1, then n is positive. • If the number in standard notation is less than 1, then n is negative.

  21. Example 5 – Express in Scientific Notation

  22. You-Try #5 – Express in Scientific Notation

  23. Example 6 – Multiply in Scientific Notation

  24. You-Try #6 – Multiply in Scientific Notation

  25. Dimensional Analysis • Performing operations with units is called dimensional analysis. • Units behave in equations the same way that variables do.

  26. Example 7 • Using the formula d=vt (distance = velocity times time), calculate how long it takes light from the sun to reach Earth, a distance of 1.5x1011 m. Light travels at a velocity of 3.0x108 m/s.

  27. You-Try #7 • Using the formula d=vt (distance = velocity times time), calculate how long it takes light from the sun to reach Mars, a distance of 2.3x1011 m. Light travels at a velocity of 3.0x108 m/s.

  28. Assignment • Page 226 #19-59 odd

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