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Chapter 6 Review: Section 1 - Using Properties of Exponents

Notes
  1. Properties of Exponents
    1. If a and b are real numbers and m and n are integers, the the following properties of exponents can be used, in any order so long as orders of operation are considered.
      1. Product of Powers
        am * aN = am + n
      2. Power of a Power
        (am)n = amn
      3. Power of a Product
        (ab)m = am * bm
      4. Negative Exponent
        a-m = 1 / (am); a <> 0
      5. Zero Exponent
        a0 = 1; a <> 0
      6. Quotient of Powers
        am / an = am - n; a <> 0
      7. Powers of a Quotient
        (a / b)m = am / bm; b <> 0
  1. Scientific Notation
    1. Scientific notation is used when making calculations with very large numbers.
    2. Numbers in scientific notation are written as c * 10n, where 1 <= c < 10, and n is an integer.
      1. To add and subtract numbers in scientific notation, convert the numbers to have the same n by moving decimal points and changing powers accordingly and add or subtract c1 and c2.
      2. Because the power always has a base of 10, multiplying and dividing numbers in scientific notation is easy due to the product of powers and quotient of powers properties. To multiply numbers in scientific notation, just multiply c1 and c2 and add the exponents.
      3. To divide numbers in scientific notation, just divide c1 by c2 and subtract the exponents.

Practice Quiz

Evaluate or simplify.
  1. (94)2
  2. 33 + 43
  3. 33 * 33
  4. 58 / 511
  5. (5x2y2)7
  6. (x8 / xy)2
Write in scientific notation.
  1. .000062
  2. 3,203,000,000,000
Solve.
  1. x = (1.2 * 107) / (4.4 * 10-11)
  2. x = (7.2 * 1011) * (3.01 * 104)

Answers
  1. 43,046,721
  2. 91
  3. 729
  4. 1 / 125
  5. 78,125x14y14
  6. x14 / y2
  7. 6.2 * 10-5
  8. 3.203 * 1012
  9. 5.28 * 1018
  10. 21.672 * 1015

Sections

Section 1 - Using Properties of Exponents
Section 2 - Evaluating & Graphing Polynomial Functions
Section 3 - Adding, Subtracting, & Multiplying Polynomials
Section 4 - Factoring & Solving Polynomial Equations
Section 5 - The Remainder & Factor Theorems
Section 6 - Finding Rational Zeroes
Section 7 - Using the Fundamental Theorem of Algebra
Chapter 6 Review Home



Steven N. Jacowski, December 18, 2002
Mrs. Gould's 3rd Hour CAT Class
Craig High School		blank
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