Answer
$\frac{\sqrt{3}}{27}$
Work Step by Step
Substitute $\frac{-5}{2}$ to x.
$f(\frac{-5}{2})$
$=3^{\frac{-5}{2}}$
Use the rule $a^{-b}=\frac{1}{a^b}, b\gt0$.
$=\frac{1}{3^{\frac{5}{2}}}$
$=\frac{1\times3^{\frac{1}{2}}}{3^{\frac{5}{2}}\times3^{\frac{1}{2}}}$
Rationalize the denominator by multiplying $3^{\frac{1}{2}}$ to the numerator and denominator.
$=\frac{3^{\frac{1}{2}}}{3^{\frac{6}{2}}}$
Simplify.
$=\frac{3^{\frac{1}{2}}}{3^3}$
$=\frac{\sqrt{3}}{27}$
