Đáp án:
Giải thích các bước giải:
Bài 1:
a/ $(\frac{7}{8})^2 . (\frac{7}{8})^3$
$=(\frac{7}{8})^5$
$=\frac{7^5}{8^5}$
$=\frac{16807}{32768}$
b/ $(\frac{-4}{5})^{100}.(\frac{5}{4})^{100}$
$=\frac{4^{100}}{5^{100}}.\frac{5^{100}}{4^{100}}$
$=1$
c/ $(\frac{1}{2})^3:(\frac{1}{8})^4$
$=\frac{1}{2^3}.\frac{8^4}{1}$
$=\frac{1}{8}.8^4$
$=8^3$
$=512$
d/ $(\frac{3}{2})^5.(\frac{2}{3})^6$
$=\frac{3^5}{2^5}.\frac{2^6}{3^6}$
$=\frac{2}{3}$
e/ $(5^{2020}+5^{2019}):5^{2019}$
$=5^{2020}:5^{2019}+5^{2019}:5^{2019}$
$=5+1$
$=6$
Bài 2:
a/ $\frac{2^{2x}}{8}=2^7$
$2^{2x}=2^7.2^3$
$2^{2x}=2^{10}$
$2x=10$
$x=5$
b/ $(-2)^{3x+1}=\frac{1}{81}$
Bạn xem lại đề thử !!!
c/ $(2x+1)^2=\frac{16}{25}$
=> \(\left[ \begin{array}{l}2x+1=\frac{4}{5}\\2x+1=-\frac{4}{5}\end{array} \right.\)
=> \(\left[ \begin{array}{l}x=-\frac{1}{10}\\x=-\frac{9}{10}\end{array} \right.\)
d/ $(3x-1)^3=\frac{-27}{8}$
=> $3x-1 = \frac{-3}{2}$
=> $x = -\frac{-1}{6}$
e/ $(\frac{2}{3})^x=(\frac{8}{27})^2$
=> $(\frac{2}{3})^x=[(\frac{2}{3})^3]^2$
=> $(\frac{2}{3})^x=(\frac{2}{3})^6$
=> $x = 6$
f/ $(\frac{16}{25})^{x+1}=(\frac{64}{125})^3$
=> $(\frac{16}{25})^{x+1}=[(\frac{4}{5})^3]^3$
=> $[(\frac{4}{5}^2]^{x+1}=(\frac{4}{5})^9$
=> $(\frac{4}{5})^{2x+2}=(\frac{4}{5})^9$
=> $2x+2=9$
=> $2x=7$
=> $x=\frac{7}{2}$
Chúc bạn học tốt !!!!
