Question

Compute the exact value of the function for the given x-value without using a calculator.F(x)=6^x for x = -3

Answer 1

$\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ f(x)=6^x\qquad \boxed{x=-3}\qquad \implies f(-3)=6^{-3}\implies f(-3)=\cfrac{1}{6^3} \\\\\\ f(-3)=\cfrac{1}{6\cdot 6\cdot 6}\implies f(-3)=\cfrac{1}{36\cdot 6}\implies f(-3)=\cfrac{1}{216}$