a) . = = = = = 9. b) : = = = = = = 8. c) + = + = + = + = + = 40. d) - = - = - = - = 121.

Bài 1 (SGK trang 55)

Gửi bởi: Sách Giáo Khoa Vào 26 tháng 12 2018 lúc 11:13:34

Lý thuyết

Câu hỏi

Tính:

$a)\ 9^{\dfrac{2}{5}}.27^{\dfrac{2}{5}}$

$b)\ 144^{\dfrac{3}{4}}:9^{\dfrac{3}{4}}$

$c)\ (\dfrac{1}{16})^{-0,75}+(0,25)^{\dfrac{-5}{2}}$

$d)\ (0,04)^{-1,5}-(0,125)^{\dfrac{-2}{3}} $

Hướng dẫn giải

a) $9^{\frac{2}{5}}$ . $27^{\frac{2}{5}}$ = $\left ( 9.27 \right )^{\frac{2}{5}}$ = $\left ( 3^{2}.3^{3} \right )^{\frac{2}{5}}$ = $\left ( 3^{5\frac{2}{5}} \right )$ = $3^{2}$ = 9.

b) $144^{\frac{3}{4}}$ : $9^{\frac{3}{4}}$ = $\left ( 144:9^{\frac{3}{4}} \right )$ = $\left ( \left ( \frac{12}{3} \right )^{2} \right )^{\frac{3}{4}}$ = $\left ( 4^{2\frac{3}{4}} \right )$ = $4^{\frac{3}{2}}$ = $2^{3}$ = 8.

c) $\left ( \frac{1}{16} \right )^{-0,75}$ + $\left ( 0,25 \right )^{\frac{-5}{2}}$ = $16^{0,75}$ + $\left ( \frac{1}{4} \right )^{\frac{-5}{2}}$ = $\left ( 2^{4} \right )^{0,75}$ + $4^{2,5}$ = $2^{4.0,75}$ + $2^{2.2,5}$ = $2^{3}$ + $2^{5}$ = 40.

d) $\left ( 0,04 \right )^{-1,5}$ - $\left ( 0,125 \right )^{\frac{-2}{3}}$ = $\left ( \frac{4}{100} \right )^{-1,5}$ - $\left ( \frac{125}{1000} \right )^{\frac{-2}{3}}$ = $\left ( \frac{100}{4} \right )^{1,5}$ - $8^{\frac{2}{3}}$ = $5^{2. 1,5}$ - $\left 2^{3\frac{2}{3}} \right$ = 121.