Question

Given that 3×√27=3^n find n

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\\\\ 3√(27)=3^n\implies √((3^2)27)=3^n\implies √((3^2)3^3)=3^n\implies \sqrt{3^(2+3)}=3^n \\\\\\ √(3^5)=3^n\implies \sqrt[2]{3^5}=3^n\implies 3^{(5)/(2)}=3^n\implies \cfrac{5}{2}=n`