Question

[Trần Bảo Thiên Hương]

 

Answer 1

[HT.Phong (9A5)]

Bài 4.2:

\(a.\left(\dfrac{1}{4}\right)^3\cdot\left(\dfrac{1}{8}\right)^2\\ =\left[\left(\dfrac{1}{2}\right)^2\right]^3\cdot\left[\left(\dfrac{1}{2}\right)^3\right]^2\\ =\left(\dfrac{1}{2}\right)^6\cdot\left(\dfrac{1}{2}\right)^6\\ =\left(\dfrac{1}{2}\right)^{12}\\ b.25\cdot5^3\cdot\dfrac{1}{625}\cdot5^3\\ =5^2\cdot5^3\cdot\dfrac{1}{5^4}\cdot5^3\\ =5^8\cdot\dfrac{1}{5^4}\\ =5^4\\ c.4^2\cdot32:2^3\\ =\left(2^2\right)^2\cdot2^5:2^3\\ =2^4\cdot2^5:2^3\\ =2^{4+5-3}\\ =2^6\\ d.5^6\cdot\dfrac{1}{20}\cdot2^2\cdot3^3:125\\ =\left(\dfrac{1}{20}\cdot2^2\cdot5\right)\cdot5^5\cdot3^3:5^3\\ =5^2\cdot3^3\)

Answer 2

[Nguyễn Lê Phước Thịnh]

bài 4.3:

a: \(\dfrac{4^6\cdot9^5+6^9\cdot120}{8^4\cdot3^{12}-6^{11}}=\dfrac{2^{12}\cdot3^{10}+2^{12}\cdot3^{10}\cdot5}{2^{12}\cdot3^{12}-2^{11}\cdot3^{11}}\)

\(=\dfrac{2^{12}\cdot3^{10}\left(1+5\right)}{2^{11}\cdot3^{11}\left(2\cdot3-1\right)}=\dfrac{2}{3}\cdot\dfrac{6}{5}=\dfrac{12}{15}=\dfrac{4}{5}\)

b: \(\dfrac{9\cdot5^{20}\cdot27^9-3\cdot9^{15}\cdot25^9}{7\cdot3^{29}\cdot125^6-3\cdot3^9\cdot15^{19}}\)

\(=\dfrac{3^2\cdot5^{20}\cdot3^{27}-3\cdot3^{30}\cdot5^{18}}{7\cdot3^{29}\cdot5^{18}-3^{10}\cdot3^{19}\cdot5^{19}}\)

\(=\dfrac{3^{29}\cdot5^{18}\left(5^2-3^2\right)}{3^{29}\cdot5^{18}\left(7-5\right)}=\dfrac{16}{2}=8\)