Find \(\alpha\) and \(\beta\) such that x\(\frac{3}{8}\) x y\(\frac{-6}{7}\) x (\(\frac{y^{\frac{9}{7}}}{x^{\frac{45}{8}}}\))\(\frac{1}{9}\) = \(\frac{y^{\alpha}}{y^{\beta}}\)
A. \(\alpha\) = 1, \(\beta\) = \(\frac{5}{7}\) B. \(\alpha\)= 1, \(\beta\) = -\(\frac{5}{7}\) C. \(\alpha\)= \(\frac{3}{5}\), \(\beta\) = -6 D. \(\alpha\)= 1, \(\beta\) = -\(\frac{3}{5}\)
Correct Answer: A
Explanation
x\(\frac{3}{8}\) x y\(\frac{-6}{7}\) x (\(\frac{y^{\frac{9}{7}}}{x^{\frac{45}{8}}}\))\(\frac{1}{9}\) = \(\frac{y^{\alpha}}{y^{\beta}}\) x\(\frac{3}{8}\) x y\(\frac{-6}{7}\) x y\(\frac{1}{7}\) = x\(\alpha\) = x\(\frac{3}{8}\) + \(\frac{5}{8}\) + y\(\frac{6}{7}\) + \(\frac{1}{7}\) = x\(\alpha\)y\(\beta\) x1y\(\frac{-5}{7}\) = x\(\alpha\)y\(\beta\) \(\alpha\) = 1, \(\beta\) = \(\frac{5}{7}\)
