Express the following fraction in simplest form, only using positive exponents. (2w^-1)/((-3w^-3))^(4) Answer Attemptiout of 2 square

To simplify the fraction \(\frac {2w^{-1}}{(-3w^{-3})^{4}}\), we need to handle the negative exponents and the power in the denominator.<br /><br />First, simplify the denominator \((-3w^{-3})^{4}\):<br />\[<br />(-3)^{4} = 81<br />\]<br />\[<br />(w^{-3})^{4} = w^{-12}<br />\]<br />So, the denominator becomes \(81w^{-12}\).<br /><br />Now, rewrite the fraction:<br />\[<br />\frac{2w^{-1}}{81w^{-12}}<br />\]<br /><br />To simplify, divide the coefficients and subtract the exponents of \(w\):<br />\[<br />\frac{2}{81} \cdot w^{-1 - (-12)} = \frac{2}{81} \cdot w^{11}<br />\]<br /><br />Thus, the simplest form of the fraction is:<br />\[<br />\frac{2w^{11}}{81}<br />\]