EXPS 1 | Lesson 2 | Making Connections (Solutions)

  1. Jane is correct because \(2^3=2\cdot2\cdot2=8\), not \(2\cdot3=6\). Thus, \(3\cdot2^3=3\cdot8=24\).
  2. \(3x^2 \neq (3x)^2\) because \((3x)^2=3^2\cdot x^2=9x^2\). Thus, \(3x^2 \neq 9x^2\).
  3. False. \(y\) was not multiplied by \(y^2\). Thus, \(3x^3y\cdot 4xy^2=12x^4y^3\)
  4. False. When raising a variable to a power, the exponent of the variable must be multiplied by that power, not added. Thus, \((3x^3yz^2)^3=27x^9y^3z^6\).
  5. True.
  6. When multiplying two expressions with the same base you add the exponents.
  7. When dividing two expressions with the same base you subtract the exponents.
  8. When raising a base with an exponent to a power you multiply the exponents.

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