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}})
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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: Option 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})