Question

HELP!! which expression is equivalent to 6z / 3^8z if z>0

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√(z)/ \sqrt[3]{8z}\implies \cfrac{6√(z)}{\sqrt[3]{8z}}\implies \cfrac{6√(z)}{\sqrt[3]{2^3z}}\implies \cfrac{6√(z)}{2\sqrt[3]{z}}\implies \cfrac{3√(z)}{\sqrt[3]{z}}\implies \cfrac{3z^{(1)/(2)}}{z^{(1)/(3)}} \\\\\\ 3z^{(1)/(2)}\cdot z^{-(1)/(3)}\implies 3z^{(1)/(2)-(1)/(3)}\implies 3z^{(3-2)/(6)}\implies 3z^{(1)/(6)}\implies 3\sqrt[6]{z}`