\(\frac{2^6.9^2}{6^4.8^3}\)
K
Khách
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H9
HT.Phong (9A5)
CTVHS
12 tháng 8 2023
a) \(A=\dfrac{2^6\cdot9^2}{6^4\cdot8}\)
\(=\dfrac{2^6\cdot\left(3^2\right)^2}{3^4\cdot2^4\cdot2^3}\)
\(=\dfrac{2^6\cdot3^4}{3^4\cdot2^7}\)
\(=\dfrac{1}{2}\)
b) \(B=\dfrac{2^{13}\cdot3^7}{2^{15}\cdot3^2\cdot9^2}\)
\(=\dfrac{2^{13}\cdot3^7}{2^{15}\cdot3^2\cdot\left(3^2\right)^2}\)
\(=\dfrac{2^{13}\cdot3^7}{2^{15}\cdot3^6}\)
\(=\dfrac{3}{2^2}\)
\(=\dfrac{3}{4}\)
15 tháng 9 2019
1
a) \(\frac{2^2.9^2}{6^4.8}\)\(=\frac{2^2+\left(3^2\right)^2}{\left(2.3\right)^4.2^3}\)\(=\frac{3^4}{2^4.3^4.2}=\frac{1}{2^4.2}=\frac{1}{2^5}=\frac{1}{32}\)
b)\(\frac{3^{10}.2^1}{16.4^3.243}=\frac{3^{10}.2^1}{2^4.4^3.3^5}=\frac{3^5}{2^3.4^3}=\frac{3^5}{\left(2.4\right)^3}\)\(=\frac{3^5}{8^3}=\frac{243}{512}\)
HM
Rút gọn phân số:
\(\frac{1.2+1.4+3.6+4.8}{2.3+4.6+6.9+8.12}\)
Làm giúp mk bài này nha!Cảm ơn mn nhiều!
3
20 tháng 4 2020
\(\frac{1.2+1.4+3.6+4.8}{2.3+4.6+6.9+8.12}\)
=\(\frac{1.2}{2.3}\)+\(\frac{1.4}{4.6}\)+\(\frac{3.6}{6.9}\)+\(\frac{4.8}{8.12}\)
= \(\frac{1}{3}\)+\(\frac{1}{6}\)+\(\frac{1}{3}\)+\(\frac{1}{3}\)
= \(\frac{2}{6}+\frac{1}{6}+\frac{2}{6}+\frac{2}{6}\)
=\(\frac{7}{6}\)
20 tháng 4 2020
Mình nghĩ đề bài phải là:
\(\frac{1.2+2.4+3.6+4.8}{2.3+4.6+6.9+8.12}\) *2.3 + 4.6 + 6.9 + 8.12 = 3.(1.2 + 2.4 + 3.6 + 4.8)*
\(=\)\(\frac{1\left(1.2+2.4+3.6+4.8\right)}{3\left(1.2+2.4+3.6+4.8\right)}\)
\(=\)\(\frac{1}{3}\)
PL
1
XO
1 tháng 11 2020
\(\frac{2^{12}.3^5-4^6.9^2}{\left(2^2.3\right)^6}=\frac{2^{12}.3^5-\left(2^2\right)^6.\left(3^2\right)^2}{2^{12}.3^6}=\frac{2^{12}.3^5-2^{12}.3^4}{2^{12}.3^6}=\frac{2^{12}\left(3^5-3^4\right)}{2^{12}.3^6}\)
\(=\frac{2^{12}.3^4\left(3-1\right)}{2^{12}.3^6}=\frac{2^{12}.3^4.2}{2^{12}.3^6}=\frac{2^{13}.3^4}{2^{12}.3^6}=\frac{2}{3^2}=\frac{2}{9}\)
20 tháng 11 2018
Gợi ý : Phân tích hết ra thành tích các thừa số nguyên tố rồi đặt cái chung ra ngoài
-> rút gọn
-> kết quả
P/S : bài này cx ko dài lắm nhưg lười ^^
7 tháng 5 2018
\(=\frac{2^{12}.2^5-2^{12}.3^4}{2^{12}.3^6+2^{12}.3^5}-\frac{5^{10}.7^3-5^{10}.7^4}{5^9.7^3+5^9.2^3.7^3}\)
\(=\frac{2^{12}.3^4.\left(3-1\right)}{2^{12}.3^5.\left(3+1\right)}-\frac{5^{10}.7^3.\left(1-7\right)}{5^9.7^3.\left(1+2^3\right)}\)
\(=\frac{2^{12}.3^4.2}{2^{12}.3^5.4}-\frac{5^{10}.7^3.\left(-6\right)}{5^9.7^3.9}\)
\(=\frac{1}{6}-\frac{-10}{3}\)
\(\frac{1}{6}-\frac{-20}{6}=\frac{7}{2}\)
3 tháng 10 2019
TA có\(\frac{2^{12}.3^5.4^6.9^2}{\left(2^2.3\right)^6+8^4.3^5}-\frac{5^{10}.7^3-25^5.49^2}{\left(125.7\right)^3}\)
=\(\frac{2^{12}.3^5.2^{12}.3^4}{2^{12}.3^6+2^{12}.3^5}-\frac{5^{10}.7^3-5^{10}.7^4}{5^9.7^3}\)
=\(\frac{2^{24}.3^9}{2^{12}.3^5.\left(3+1\right)}-\frac{5^{10}.7^3.\left(1-7\right)}{5^9.7^3}\)
=\(2^{20}.3^4-30\)
K
4 tháng 7 2017
\(B=\frac{2^{13}.3^5-4^6.9^2}{\left(2^2.3\right)^6+8^4.3^5}-\frac{5^{10}.7^3-25^5.49^2}{\left(125.7\right)^3+5^9.14^3}\)
\(=\frac{2^{13}.3^5-\left(2^2\right)^6.\left(3^2\right)^2}{2^{12}.3^6+\left(2^3\right)^4.3^5}-\frac{5^{10}.7^3-\left(5^2\right)^5.\left(7^2\right)^2}{\left(5^3.7\right)^3+5^9.\left(2.7\right)^3}\)
\(=\frac{2^{13}.3^5-2^{12}.3^4}{2^{12}.3^6+2^{12}.3^5}-\frac{5^{10}.7^3-5^{10}.7^4}{5^9.7^3+5^9.2^3.7^3}\)
\(=\frac{2^{12}.3^4\left(2.3-1\right)}{2^{12}.3^5\left(3+1\right)}-\frac{5^{10}.7^3\left(1-7\right)}{5^9.7^3.\left(1+2^3\right)}\)
\(=\frac{2^{12}.3^4.5}{2^{12}.3^5.4}-\frac{5^{10}.7^3.\left(-6\right)}{5^9.7^3.9}\)
\(=\frac{5}{12}-\frac{-10}{3}=\frac{5}{12}+\frac{40}{12}=\frac{45}{12}=\frac{15}{4}=3\frac{3}{4}\)
14 tháng 11 2018
\(B=\frac{2^{12}.3^5-4^6.9^2}{\left(2^2.3\right)^6+8^4.3^5}-\frac{5^{10}.7^3-25^5.49^2}{\left(125.7\right)^3+5^9.14^3}\)
\(=\frac{2^{12}.3^5-2^{12}.3^6}{2^{12}.3^6+2^{12}.3^5}-\frac{5^{10}.7^3-5^{10}.7^4}{5^9.7^3+5^9.2^3.7^3}\)
\(=\frac{2^{12}.3^5.\left(1-3\right)}{2^{12}.3^6.\left(3+1\right)}-\frac{5^9.7^3.\left(1-7\right)}{5^9.7^3\left(1+2^3.1\right)}\)
\(=\frac{-1}{2}-\frac{-2}{3}=\frac{-7}{6}\)
\(\frac{2^6.9^2}{6^4.8^3}=\frac{5184}{663552}=\frac{1}{128}\)
Học tốt!!!
\(\frac{2^6.9^2}{6^4.8^3}\)
\(=\frac{2^6.\left(3^2\right)^2}{\left(2.3\right)^4.\left(2^3\right)^3}=\frac{2^6.3^4}{2^4.3^4.2^9}\)
\(=\frac{2^6.3^4}{2^{13}.3^4}=\frac{2^6}{2^{13}}=\frac{1}{2^7}=\frac{1}{128}\)