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6^5 ÷ 6^-3
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\[\Large \frac{ a^{m} }{ a^{n} } = a^{m-n}\]
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http://2.bp.blogspot.com/_ViOqoLbfiLQ/THWS177DVwI/AAAAAAAAANE/1QP4DymkDi0/s1600/exponent+rules.png
If you use these rules, the problems aren't that hard
\[\begin{array}{|l||c|} \hline \text{Step} &\text{Algebra} &\text{Rule}\\ \hline 1 & 6^5 \div6^{-3} &\text{Given}\\ \hline 2 & 6^5 \div \frac{1}{6^3}& a^{-b} = \frac{1}{a^b}\\ \hline 3 & 6^5 \times 6^3 & a\div \frac{b}{c} = a \times \frac{c}{b}\\ \hline 4 & 6^{5 + 3} & a^b \times a^c = a^{b + c}\\ \hline 5 & 6^8 & \text{Conclusion}\\ \hline \end{array}\]
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