Question

Write 6^4÷√6 as a single power of 6.

Answer 1

$~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] ~\dotfill\\\\ 6^4\div \sqrt{6}\implies \cfrac{6^4}{\sqrt{6}}\implies \cfrac{6^4}{6^{\frac{1}{2}}}\implies 6^4\cdot 6^{-\frac{1}{2}} \\\\\\ 6^{4-\frac{1}{2}}\implies 6^{\frac{8-1}{2}}\implies 6^{\frac{7}{2}}$