Rút gọn
a) \(\frac{45^{-10}.5^{20}}{75^{15}}\)
b) \(\frac{2^{15}.9^4}{6^6.8^2}\)
làm ơn giúp mik vs ạ mik đag cần rất gấp
K
Khách
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Những câu hỏi liên quan
13 tháng 9 2016
a) \(\frac{45^{10}.5^{20}}{75^{15}}\)
=
\(\frac{\left(5.9\right)^{10}.5^{20}}{\left(5.15\right)^{15}}\)
= \(\frac{5^{10}.9^{10}.5^{20}}{5^{15}.15^{15}}\)
= \(\frac{5^{10}.3^{20}.5^{20}}{5^{15}.15^{15}}\)
= \(\frac{5^{10}.15^{20}}{5^{15}.15^{15}}\)
= \(\frac{15^5}{5^5}\)
= \(\frac{3^5.5^5}{5^5}\)
= \(3^5\)
b) \(\frac{\left(0,8\right)^5}{\left(0,4\right)^6}\)
= \(\frac{\left(0,4\right)^5.2^5}{\left(0,4\right)^6}\)
= \(\frac{2^5}{0,4}\)
= \(2^5\) : 0,4
(=) 32 : \(\frac{2}{5}\)
= 90
c) \(\frac{2^{15}.9^4}{6^6.8^3}\)
= \(\frac{2^{15}.\left(3^2\right)^4}{\left(2.3\right)^6.\left(2^3\right)^3}\)
= \(\frac{2^{15}.3^8}{2^6.3^6.2^9}\)
= \(3^2\)
21 tháng 7 2016
tớ cũng đang học cái đấy nè
225^10
a = _________ = 3^10
75^10
2^15 * 3^8 2^15 * 3^8
c= _____________= -------------------- =2^3 * 3^5
2^3 * 3^3 * 2^9 2^12 * 3^3
N
2
2 tháng 8 2018
\(9^8:3^2=3^{16}:3^2=3^{14}\)
\(\frac{45^{10}.5^{20}}{75^{15}}=\frac{\left(5.3^2\right)^{10}.5^{20}}{\left(5^2.3\right)^{15}}=\frac{5^{10}.3^{20}.5^{20}}{5^{30}.3^{15}}=3^5\)
\(\frac{2^{15}.9^4}{6^6.8^3}=\frac{2^{15}.3^8}{2^6.3^6.2^9}=\frac{2^{15}.3^8}{2^{15}.3^6}=3^2=9\)
2 tháng 8 2018
1) 98 : 32 =(32)8:32=32.8:32=316:32=316-2=314
2) (4510.520)/7515=[(5.23)10.520]/(53)15=(510.23.10.520)/53.15=(530.230)/545=230/515=(22)15/515=(4/5)15
3) (215.94)/(66.83)=[215.(32)4]/[(2.30)....
Bạn làm tương tự
hk tốt nha!!!
BV
2
MT
1 tháng 7 2015
a)\(\frac{45^{10}.5^{20}}{75^{15}}=\frac{\left(3^2.5\right)^{10}.5^{20}}{\left(3.5^2\right)^{15}}=\frac{\left(3^2\right)^{10}.5^{10}.5^{20}}{3^{15}.\left(5^2\right)^{15}}=\frac{3^{20}.5^{30}}{3^{15}.5^{30}}=3^5=243\)
b)\(\frac{2^{15}.9^4}{6^6.8^3}=\frac{2^{15}.\left(3^2\right)^4}{\left(3.2\right)^6.\left(2^3\right)^3}=\frac{2^{15}.3^8}{3^6.2^6.2^9}=\frac{2^{15}.3^8}{3^6.2^{15}}=3^2=9\)
PA
22 tháng 7 2016
a.
\(\frac{45^{10}\times5^{20}}{75^{15}}=\frac{\left(3^2\times5\right)^{10}\times5^{20}}{\left(3\times5^2\right)^{15}}=\frac{3^{20}\times5^{10}\times5^{20}}{3^{15}\times5^{30}}=3^5=243\)
b.
\(\frac{\left(0,8\right)^5}{\left(0,4\right)^6}=\frac{\left(0,8\right)^5}{\left(0,4\right)^5}\times\frac{1}{\left(0,4\right)}=\left(\frac{0,8}{0,4}\right)^5\times\frac{1}{\frac{4}{10}}=2^5\times\frac{5}{2}=2^4\times5=16\times5=80\)
c.
\(\frac{2^{15}\times9^4}{6^6\times8^3}=\frac{2^{15}\times\left(3^2\right)^4}{\left(2\times3\right)^6\times\left(2^3\right)^3}=\frac{2^{15}\times3^8}{2^6\times3^6\times2^9}=3^2=9\)
Chúc bạn học tốt ^^
6 tháng 8 2020
Bài làm:
Ta có: \(\frac{7.6^{10}.2^{20}.3^6-2^{19}.6^{15}}{9.6^{19}.2^9-4.3^{17}.2^{26}}\)
\(=\frac{7.2^{10}.3^{10}.2^{20}.3^6-2^{19}.2^{15}.3^{15}}{3^2.2^{19}.3^{19}.2^9-2^2.3^{17}.2^{26}}\)
\(=\frac{2^{30}.3^{16}.7-2^{34}.3^{15}}{2^{28}.3^{21}-2^{28}.3^{17}}\)
\(=\frac{2^{30}.3^{15}\left(3.7-2^4\right)}{2^{28}.3^{17}\left(3^4-1\right)}\)
\(=\frac{2^2\left(21-16\right)}{3^2\left(81-1\right)}\)
\(=\frac{2^2.5}{3^2.80}\)
\(=\frac{1}{36}\)
NV
Nguyễn Việt Lâm
Giáo viên
21 tháng 9 2019
\(B=\left(2\sqrt{9.5}-\frac{3}{2}\sqrt{4.5}+\frac{\sqrt{5.15}}{\sqrt{15}}\right).\frac{3}{\sqrt{10}}\)
\(=\left(6\sqrt{5}-3\sqrt{5}+\sqrt{5}\right).\frac{3}{\sqrt{5}.\sqrt{2}}\)
\(=\frac{4\sqrt{5}.3}{\sqrt{5}.\sqrt{2}}=\frac{12}{\sqrt{2}}=6\sqrt{2}\)
Ở câu a) số mũ lúc nào cug dương mà bạn ( 45-10 = 4510). Nếu số mũ là dương thì:
a)\(\frac{45^{10}.5^{20}}{75^{15}}\)
= \(\frac{\left(3^2.5\right)^{10}.5^{20}}{\left(3.5^2\right)^{15}}\)
= \(\frac{3^{20}.5^{10}.5^{20}}{3^{15}.5^{30}}\)
= \(\frac{3^{20}.5^{30}}{3^{15}.5^{30}}\)
= \(\frac{3^5.1}{1.1}\)
= \(\frac{243}{1}\)
= 243
b)\(\frac{2^{15}.9^4}{6^6.8^2}\)
= \(\frac{2^{15}.\left(3^2\right)^4}{\left(2.3\right)^6.\left(2^3\right)^2}\)
= \(\frac{2^{15}.3^8}{2^6.3^6.2^6}\)
= \(\frac{2^{15}.3^8}{2^{12}.3^6}\)
= \(\frac{2^3.3^2}{1.1}\)
= \(\frac{8.9}{1}\)
= \(\frac{72}{1}\)
= 72
cảm ơn bn