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Section 1.1 : Integer Exponents
5. Simplify the following expression and write the answer with only positive exponents.
\[{\left( {2{w^4}{v^{ - 5}}} \right)^{ - 2}}\] 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.
\[{\left( {2{w^4}{v^{ - 5}}} \right)^{ - 2}} = {2^{ - 2}}{w^{ - 8}}{v^{10}} = \frac{{{v^{10}}}}{{{2^2}{w^8}}} = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{{{v^{10}}}}{{4{w^8}}}}}\]Note that there are several “paths” (i.e. the order in which you chose to use the properties) you can take to do the simplification. Each will end up with the same answer however and so you don’t need to get excited if you chose a different order in which to use the properties than we did here.