Bài 3 trang 13 SGK Toán 11 tập 2 – Chân trời sáng tạo

Đề bài

Rút gọn các biểu thức sau \(\left( {a > 0,b > 0} \right)\):

a) \({a^{\frac{1}{3}}}{a^{\frac{1}{2}}}{a^{\frac{7}{6}}}\);

b) \({a^{\frac{2}{3}}}{a^{\frac{1}{4}}}:{a^{\frac{1}{6}}}\);

c) \(\left( {\frac{3}{2}{a^{ – \frac{3}{2}}}{b^{ – \frac{1}{2}}}} \right)\left( { – \frac{1}{3}{a^{\frac{1}{2}}}{b^{\frac{3}{2}}}} \right)\).

Lời giải chi tiết

a) \({a^{\frac{1}{3}}}{a^{\frac{1}{2}}}{a^{\frac{7}{6}}} = {a^{\frac{1}{3} + \frac{1}{2} + \frac{7}{6}}} = {a^2}\)

b) \({a^{\frac{2}{3}}}{a^{\frac{1}{4}}}:{a^{\frac{1}{6}}} = {a^{\frac{2}{3} + \frac{1}{4} – \frac{1}{6}}} = {a^{\frac{3}{4}}}\)

c) \(\left( {\frac{3}{2}{a^{ – \frac{3}{2}}}{b^{ – \frac{1}{2}}}} \right)\left( { – \frac{1}{3}{a^{\frac{1}{2}}}{b^{\frac{3}{2}}}} \right) = \frac{3}{2}.\left( { – \frac{1}{3}} \right).{a^{ – \frac{3}{2} + \frac{1}{2}}}.{b^{ – \frac{1}{2} + \frac{3}{2}}} =  – \frac{1}{2}{a^{ – 1}}b =  – \frac{b}{{2{\rm{a}}}}\)