Find \(\alpha\) and \(\beta\) such that x\(\frac{3}{8}\) x y\(\frac{-6}{7}\) x (\(\frac{y^{\frac{9}{7}}}{x^{\frac{45}{8}}}\))\(\frac{1}{9}\) = \(\frac{x^{\alpha}}{y^{\beta}}\)
A
\(\alpha\) = 1, \(\beta\) = \(\frac{5}{7}\)
B
\(\alpha\)= 1, \(\beta\) = -\(\frac{5}{7}\)
C
\(\alpha\)= \(\frac{3}{5}\), \(\beta\) = -6
D
\(\alpha\)= 1, \(\beta\) = -\(\frac{3}{5}\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
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, \(\beta\) = \(\frac{5}{7}\)
Source: Myschool Past Questions Archive (Record #32489)