Section 1.1 : Integer Exponents
8. Simplify the following expression and write the answer with only positive exponents.
\[\frac{{{{\left( {2{p^2}} \right)}^{ - 3}}{q^4}}}{{{{\left( {6q} \right)}^{ - 1}}{p^{ - 7}}}}\] Show SolutionThere is not really a whole lot to this problem. All we need to do is use the properties from this section to do the simplification.
\[\frac{{{{\left( {2{p^2}} \right)}^{ - 3}}{q^4}}}{{{{\left( {6q} \right)}^{ - 1}}{p^{ - 7}}}} = \frac{{{2^{ - 3}}{p^{ - 6}}{q^4}}}{{{6^{ - 1}}{q^{ - 1}}{p^{ - 7}}}} = \frac{{{6^1}{p^7}{q^4}{q^1}}}{{{2^3}{p^6}}} = \frac{{6{p^1}{q^5}}}{8} = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{{3p{q^5}}}{4}}}\]Don’t try to do use too many properties all at once. Sometimes it is very easy to use too many properties all in one step and make a mistake. There’s nothing wrong with using only a single property or two with each step.