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Section 1-1 : Integer Exponents

For problems 1 – 4 evaluate the given expression and write the answer as a single number with no exponents.

  1. \( - {6^2} + 4 \cdot {3^2}\) Solution
  2. \(\displaystyle \frac{{{{\left( { - 2} \right)}^4}}}{{{{\left( {{3^2} + {2^2}} \right)}^2}}}\) Solution
  3. \(\displaystyle \frac{{{4^0} \cdot {2^{ - 2}}}}{{{3^{ - 1}} \cdot {4^{ - 2}}}}\) Solution
  4. \({2^{ - 1}} + {4^{ - 1}}\) Solution

For problems 5 – 9 simplify the given expression and write the answer with only positive exponents.

  1. \({\left( {2{w^4}{v^{ - 5}}} \right)^{ - 2}}\) Solution
  2. \(\displaystyle \frac{{2{x^4}{y^{ - 1}}}}{{{x^{ - 6}}{y^3}}}\) Solution
  3. \(\displaystyle \frac{{{m^{ - 2}}{n^{ - 10}}}}{{{m^{ - 7}}{n^{ - 3}}}}\) Solution
  4. \(\displaystyle \frac{{{{\left( {2{p^2}} \right)}^{ - 3}}{q^4}}}{{{{\left( {6q} \right)}^{ - 1}}{p^{ - 7}}}}\) Solution
  5. \({\left( {\displaystyle \frac{{{z^2}{y^{ - 1}}{x^{ - 3}}}}{{{x^{ - 8}}{z^6}{y^4}}}} \right)^{ - 4}}\) Solution