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8.9: Chapter 8 Review

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Define the following words.

  1. Exponent
  2. Geometric Sequence

Use the product properties to simplify the following expressions.

  1. 5 \cdot 5 \cdot 5 \cdot 5
  2. (3x^2y^3) \cdot (4xy^2)
  3. a^3 \cdot a^5 \cdot a^6
  4. (\gamma^3)^5
  5. (x \cdot x^3 \cdot x^5)^{10}
  6. (2a^3 b^3)^2

Use the quotient properties to simplify the following expressions.

  1. \frac{c^5}{c^3}
  2. \frac{a^6}{a}
  3. \frac{a^5b^4}{a^3b^2}
  4. \frac{x^4 y^5 z^2}{x^3 y^2 z}

Simplify the following expressions.

  1. \frac{6^5}{6^5}
  2. \frac{\gamma^2}{\gamma^5}
  3. \frac{7^3}{7^6}
  4. \frac{2}{\chi^3}
  5. \sqrt[4]{\alpha^3}
  6. \left(a^{\frac{1}{3}}\right)^2
  7. \left(\frac{x^2}{y^3}\right)^{\frac{1}{3}}

Write the following in scientific notation.

  1. 557,000
  2. 600,000
  3. 20
  4. 0.04
  5. 0.0417
  6. 0.0000301
  7. The distance from the Earth to the moon: 384,403 km
  8. The distance from Earth to Jupiter: 483,780,000 miles
  9. According to the CDC, the appropriate level of lead in drinking water should not exceed 15 parts per billion (EPA’s Lead & Copper Rule).

Write the following in standard notation.

  1. 3.53 \times 10^3
  2. 89 \times 10^5
  3. 2.12 \times 10^6
  4. 5.4 \times 10^1
  5. 7.9 \times 10^{-3}
  6. 4.69 \times 10^{-2}
  7. 1.8 \times 10^{-5}
  8. 8.41 \times 10^{-3}

Make a graph of the following exponential growth/decay functions.

  1. \gamma=3 \cdot (6)^x
  2. \gamma=2 \cdot \left(\frac{1}{3}\right)^x
  3. Marissa was given 120 pieces of candy for Christmas. She ate one-fourth of them each day. Make a graph to find out in how many days Marissa will run out of candy.
  4. Jacoby is given $1500 for his graduation. He wants to invest it. The bank gives a 12% investment rate each year. Make a graph to find out how much money Jacoby will have in the bank after six years.

Determine what the common ratio is for the following geometric sequences to finish to sequence.

  1. 1, 3, __, __, 81
  2. __, 5, __, 125, 625
  3. 7, __, 343, 2401, __
  4. 5, 1.5, __, 0.135, __
  5. The population of ants in Ben’s room increases three times daily. He starts with only two ants. Make a geometric graph to determine how many ants will be in Ben’s room at the end of a 30-day month if he does not take care of the problem.

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