Question

Which line did leah go wrong at and why? Please show explanation to how to solve the problem. Thank you in advance :)

Answer 1

`2^(2x-3)~~ = ~~\left( \cfrac{1}{16} \right)^(3x+9) \\\\\\ 2^(2x-3)~~ = ~~\left( \cfrac{1}{2^4} \right)^(3x+9) \\\\\\ \boxed{2^(2x-3)~~ = ~~\left( 2^(-4) \right)^(3x+9)} \\\\\\ 2^(2x-3)~~ = ~~2^(-4(3x+9))\implies 2^(2x-3)~~ = ~~2^(-12x-36)\implies 2x-3=-12x-36 \\\\\\ 14x-3=-36\implies 14x=-33\implies {\Large \begin{array}{llll} x=\cfrac{-33}{14} \end{array}}`

Check the picture below.