Bài 3 trang 13

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) $\left(\frac{3}{2}{a}^{-\frac{3}{2}}{b}^{-\frac{1}{2}}\right)\left(-\frac{1}{3}{a}^{\frac{1}{2}}{b}^{\frac{3}{2}}\right)$.

$=\frac{3}{2}.\left(-\frac{1}{3}\right).a^{-\frac{3}{2}+\frac{1}{2}}.b^{-\frac{1}{2}+\frac{3}{2}}$

$=-\frac{1}{2}{a}^{-1}b=-\frac{b}{2a}$.