Question

Write 6^4÷√6 as a single power of 6.

Answer 1

`~\hspace{7em}\textit{rational exponents} \\\\ a^{( n)/( m)} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-( n)/( m)} \implies \cfrac{1}{a^{( n)/( m)}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] ~\dotfill\\\\ 6^4/ √(6)\implies \cfrac{6^4}{√(6)}\implies \cfrac{6^4}{6^{(1)/(2)}}\implies 6^4\cdot 6^{-(1)/(2)} \\\\\\ 6^{4-(1)/(2)}\implies 6^{(8-1)/(2)}\implies 6^{(7)/(2)}`