Question

20 points!
Show work please! I have no idea how to do this, haha.

Answer 1

`\bf \left.\qquad \qquad \right.\textit{negative exponents}\\\\ a^{-{ n}} \implies \cfrac{1}{a^( n)} \qquad \qquad \cfrac{1}{a^( n)}\implies a^{-{ n}} \qquad \qquad a^{{{ n}}}\implies \cfrac{1}{a^{-{{ n}}}} \\\\ -------------------------------\\\\`


`\bf 3^(5x-9)=\left( \cfrac{1}{27} \right)^(2x-8)\qquad \boxed{27=3^3}\qquad 3^(5x-9)=\left( \cfrac{1}{3^3} \right)^(2x-8) \\\\\\ 3^(5x-9)=\left( 3^(-3) \right)^(2x-8)\implies 3^(5x-9)= 3^(-3(2x-8)) \\\\\\ 3^(5x-9)= 3^(-6x+24)\impliedby \begin{array}{llll} \textit{the bases are the same, then}\\ \textit{the exponents must be the same} \end{array} \\\\\\ 5x-9=-6x+24\implies 11x=33\implies x=\cfrac{33}{11}\implies x=3`