Mobile Notice
You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width.
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.