Question

Đơn giản biểu thức sau :

\(T=\left(\sqrt[7]{\frac{a}{b}\sqrt[5]{\frac{b}{a}}}\right)^{\frac{35}{4}}\)

Answer 1

\(T=\left(\sqrt[7]{\frac{a}{b}\sqrt[5]{\frac{b}{a}}}\right)^{\frac{35}{4}}=\left\{\left[\left(\frac{b}{a}\right)^{-1}\left(\frac{b}{a}\right)^{\frac{1}{5}}\right]^{\frac{1}{7}}\right\}^{\frac{35}{4}}=\left[\left(\frac{b}{a}\right)^{-\frac{4}{5}}\right]=\frac{a}{b}\)

Answer 2

\(T=\left(\sqrt[7]{\frac{a}{b}\sqrt[5]{\frac{b}{a}}}\right)^{\frac{35}{4}}=\sqrt[4]{\left(\sqrt[7]{\frac{a}{b}\sqrt[5]{\frac{b}{a}}}\right)^{35}}=\sqrt[4]{\left(\frac{a}{b}\sqrt[5]{\frac{b}{a}}\right)^5}\)

\(=\sqrt[4]{\left(\frac{a}{b}\right)^5.\frac{b}{a}}=\sqrt[4]{\left(\frac{a}{b}\right)^4}=\frac{a}{b}\)