rút gọn :
6^9 . 2^10 + 12^10 / 2^19 . 27^3 + 15 . 4^9 . 9^4
em không biết đặc cột dọc phân số lên là nhìn nó hơi khó hẻo 1 xíu nhưng mà các cao nhân ôi~~ please mà giúp em zới đi mờ ~~~~~~ em đợi câu trả lời đấy nhá !
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TL
\(\frac{3}{5}=\frac{3x2}{5x2}=\frac{6}{10}\) (cách làm là nhan cả tử và mẫu với một số )
tương tự
\(\frac{3}{5}=\frac{6}{10}=\frac{9}{15}=\frac{12}{20}\)
HT
Tham khảo :
(Tại mik lười ko mún ghi nên bạn tham khảo cái ảnh này nhá)
1.3.77−1+3.7.99−3+7.9.1313−7+9.13.1515−9+\frac{19-13}{13.15.19}+13.15.1919−13
=\frac{1}{1.3}-\frac{1}{3.7}+\frac{1}{3.7}-\frac{1}{7.9}+\frac{1}{7.9}-\frac{1}{9.13}+\frac{1}{9.13}-\frac{1}{13.15}+\frac{1}{13.15}-\frac{1}{15.19}=1.31−3.71+3.71−7.91+7.91−9.131+9.131−13.151+13.151−15.191
=\frac{1}{1.3}-\frac{1}{15.19}=\frac{95}{285}-\frac{1}{285}=\frac{94}{285}=1.31−15.191=28595−2851=28594
b,=\frac{1}{6}.\left(\frac{6}{1.3.7}+\frac{6}{3.7.9}+\frac{6}{7.9.13}+\frac{6}{9.13.15}+\frac{6}{13.15.19}\right)b,=61.(1.3.76+3.7.96+7.9.136+9.13.156+13.15.196)
làm giống như trên
c,=\frac{1}{8}.\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{48.49.50}\right)c,=81.(1.2.31+2.3.41+3.4.51+...+48.49.501)
=\frac{1}{16}.\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{48.49.50}\right)=161.(1.2.32+2.3.42+3.4.52+...+48.49.502)
=\frac{1}{16}.\left(\frac{3-1}{1.2.3}+\frac{4-2}{2.3.4}+\frac{5-3}{3.4.5}+...+\frac{50-48}{48.49.50}\right)=161.(1.2.33−1+2.3.44−2+3.4.55−3+...+48.49.5050−48)
=\frac{1}{16}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{48.49}-\frac{1}{49.50}\right)=161.(1.21−2.31+2.31−3.41+3.41−4.51+...+48.491−49.501)
=\frac{1}{16}.\left(\frac{1}{2}-\frac{1}{2450}\right)=\frac{1}{16}.\left(\frac{1225}{2450}-\frac{1}{2450}\right)=\frac{153}{4900}=161.(21−24501)=161.(24501225−24501)=4900153
d,=\frac{5}{7}.\left(\frac{7}{1.5.8}+\frac{7}{5.8.12}+\frac{7}{8.12.15}+...+\frac{7}{33.36.40}\right)d,=75.(1.5.87+5.8.127+8.12.157+...+33.36.407)
=\frac{5}{7}.\left(\frac{8-1}{1.5.8}+\frac{12-5}{5.8.12}+\frac{15-8}{8.12.15}+...+\frac{40-33}{33.36.40}\right)=75.(1.5.88−1+5.8.1212−5+8.12.1515−8+...+33.36.4040−33)
=\frac{5}{7}.\left(\frac{1}{1.5}-\frac{1}{5.8}+\frac{1}{5.8}-\frac{1}{8.12}+\frac{1}{8.12}-\frac{1}{12.15}+...+\frac{1}{33.36}-\frac{1}{36.40}\right)=75.(1.51−5.81+5.81−8.121+8.121−12.151+...+33.361−36.401)
=\frac{5}{7}.\left(\frac{1}{5}-\frac{1}{1440}\right)=\frac{5}{7}.\left(\frac{288}{1440}-\frac{1}{1440}\right)=\frac{41}{288}=75.(51−14401)=75.(1440288−14401)=28841
P/S: . là nhân nha
Tử số= 2^19.9^3.3^3 + 5.3.2^9.2^9.9^4
= 2^19.9^3.3^3 + 5.3.2^18.9.9^3
= 2^19.9^3.3.3^2 + 5.3.2^18.3^2.9^3
= 2^18.9^3.3^2(2 + 5.) (đặt nhân tử chung)
=7.2^18.9^3.3^2
=7.2^18.9.9.9.3^2
=7.2^18.3^2.3^2.3^2.3^2
=7.2^18.3^8
Mẫu số= 6^9.2^10 + 6^10.2^10
= 6^9.2^10 + 6^10.2^10
=6^9.2^10(1+6)
=7.6^9.2^10.
=7.2^9.3^9.2^10
=7.2^19.3^9
Lấy tử số chia mẫu số ta được : 1/2.3 = 1/6
\(\dfrac{6^9.2^{10}+12^{10}}{2^{19}.27^3+15.4^9.9^4}\)
\(=\dfrac{\left(2.3\right)^9.2^{10}+\left(2^2.3\right)^{10}}{2^{19}.\left(3^3\right)^3+3.5.\left(2^2\right)^9.\left(3^2\right)^4}\)
\(=\dfrac{2^{19}.3^9+2^{20}.3^{10}}{2^{19}.3^9+5.2^{18}.3^9}\)
\(=\dfrac{2^{19}.3^9\left(1+2.3\right)}{2^{19}.3^9\left(1+5.2\right)}\)
\(=\dfrac{1+6}{1+10}=\dfrac{7}{11}\)
\(\dfrac{6^9.2^{10}+12^{10}}{2^{19}.27^3+15.4^9.9^4}\\ =\dfrac{2^9.3^9.2^{10}+\left(2^2.3\right)^{10}}{2^{19}.\left(3^3\right)^3+3.5.\left(2^2\right)^9\left(3^2\right)^4}\\ =\dfrac{2^{19}.3^9+2^{20}.3^{10}}{2^{19}.3^9+5.2^{18}.3^9}\\ =\dfrac{2^{18}.3^9.\left(2+2^2.3\right)}{2^{18}.3^9.\left(2+5\right)}\\ =\dfrac{14}{7}\\ =2\)