Cho \(\alpha \in \left( {0;\frac{\pi }{2}} \right).\) Rút gọn biểu thức \(P = {2^{{{\sin }^4}\alpha }}{2^{{{\cos }^4}\alpha }}{4^{{{\sin

Cho \(\alpha \in \left( {0;\frac{\pi }{2}} \right).\) Rút gọn biểu thức \(P = {2^{{{\sin }^4}\alpha }}{2^{{{\cos }^4}\alpha }}{4^{{{\sin }^2}\alpha {{\cos }^2}\alpha }}.\)
A. \(P = {2^{\sin \alpha cos\alpha }}\)
B. \(P = 2\)
C. \(P = {2^{\sin \alpha +cos\alpha }}\)
D. \(P = 4\)

Ta có: \({2^{{{\sin }^4}\alpha }}{.2^{{{\cos }^4}\alpha }}{.4^{{{\sin }^2}\alpha .{{\cos }^2}\alpha }} = {2^{{{\sin }^4}\alpha + {{\cos }^4}\alpha + 2.{{\sin }^2}\alpha .{{\cos }^2}\alpha }} = {2^{{{\left( {{{\sin }^2}\alpha + {{\cos }^2}\alpha } \right)}^2}}} = {2^1} = 2\)