Respuesta :
[tex]\bf ~\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] \rule{34em}{0.25pt}[/tex]
[tex]\bf f(x)=6(9)^x\qquad \boxed{x=\frac{1}{2}}\qquad \implies f\left( \frac{1}{2} \right)=6(9)^{\frac{1}{2}}\implies f\left( \frac{1}{2} \right)=6\sqrt[2]{9^1} \\\\\\ f\left( \frac{1}{2} \right)=6\sqrt{9}\implies f\left( \frac{1}{2} \right)=6(3)\implies f\left( \frac{1}{2} \right)=18[/tex]
The Answer is
[tex]f(\frac{1}{2} )= 18[/tex]
This function can be solved by using the properties of exponents
By using the rules of algebra the exponents are solved first then we will multiply.
[tex]f(x)= 6\times 9^{x}[/tex]....(1)
Substituting x= 1/2 in above equation (1)
[tex]f(\frac{1}{2} )= 6\times 9^{1/2}[/tex]
[tex]f(\frac{1}{2} )= 6\times \sqrt{9}[/tex]
[tex]Since \; \sqrt{9} = 3[/tex]
[tex]f(\frac{1}{2} )= 6\times 3[/tex]
[tex]f(\frac{1}{2} )= 18[/tex]
for more information about the functions follow the link below
https://brainly.com/question/18752815
