\(\dfrac{9^4.2^{15}}{2^6.24^3}\)
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\(\dfrac{9^4.2^{15}}{2^6.24^3}\) = \(\dfrac{9^4.2^9}{24^3}\) = \(\dfrac{2^9.3^8}{2^9.3^3}\) = 35 = 243
\(\dfrac{9^4\cdot2^{15}}{2^6\cdot24^3}=\dfrac{\left(3^2\right)^4\cdot2^{15}}{2^6\cdot\left(8\cdot3\right)^3}=\dfrac{3^8\cdot2^{15}}{2^6\cdot8^3\cdot3^3}=\dfrac{3^8\cdot2^{15}}{2^6\cdot2^9\cdot3^3}=\dfrac{3^8\cdot2^{15}}{2^{15}\cdot3^3}=3^5=243\)
a) \(2^2\cdot5^2-64:2^3\)
\(=4\cdot25-2^6:2^3\)
\(=100-2^3=100-8\)
\(=92\)
b) \(3^5\cdot9:243\)
\(=3^5\cdot9:3^5=9\)
c) \(4\cdot2^5\cdot2^3\cdot\dfrac{1}{16}\)
\(=2^{10}\cdot\dfrac{1}{2^4}=2^6\)
\(=64\)
d) \(\dfrac{11\cdot3^{22}\cdot3^7-9^{15}}{3^{28}}\)
\(=\dfrac{11\cdot3^{29}-\left(3^2\right)^{15}}{3^{28}}\)
\(=\dfrac{11\cdot3^{29}-3^{30}}{3^{28}}=\dfrac{3^{29}\left(11-3\right)}{3^{28}}\)
\(=\dfrac{3^{29}\cdot8}{3^{28}}=3\cdot8=24\)
\(=\dfrac{5\cdot2^{12}\cdot3^8-3^9\cdot2^{12}}{2^{15}\cdot3^{18}-2^{13}\cdot3^9}\)
\(=\dfrac{2^{12}\cdot3^8\left(5-3\right)}{2^{13}\cdot3^9\left(2^2\cdot3^9-1\right)}\)
\(=\dfrac{1}{3\cdot\left(4\cdot3^9-1\right)}\)
A = - 522 - { - 222 - [ - 122 - (100 - 522) + 2022] }
A = - 522 - { -222 - [- 122 - 100 + 522 ] + 2022}
A = - 522 - { -222 - { - 222 + 522 } + 2022}
A = - 522 - {- 222 + 222 - 522 + 2022}
A = -522 + 522 - 2022
A = - 2022
B = 1 + \(\dfrac{1}{2}\)(1 + 2) + \(\dfrac{1}{3}\).(1 + 2 + 3) + ... + \(\dfrac{1}{20}\).(1 + 2+ 3 + ... + 20)
B = 1+\(\dfrac{1}{2}\)\(\times\)(1+2)\(\times\)[(2-1):1+1]:2+ ... + \(\dfrac{1}{20}\)\(\times\) (20 + 1)\(\times\)[(20-1):1+1]:2
B = 1 + \(\dfrac{1}{2}\) \(\times\) 3 \(\times\) 2:2 + \(\dfrac{1}{3}\) \(\times\)4 \(\times\) 3 : 2+....+ \(\dfrac{1}{20}\) \(\times\)21 \(\times\) 20 : 2
B = 1 + \(\dfrac{3}{2}\) + \(\dfrac{4}{2}\) + ....+ \(\dfrac{21}{2}\)
B = \(\dfrac{2+3+4+...+21}{2}\)
B = \(\dfrac{\left(21+2\right)\left[\left(21-2\right):1+1\right]:2}{2}\)
B = \(\dfrac{23\times20:2}{2}\)
B = \(\dfrac{23\times10}{2}\)
B = 23
\(=\dfrac{-12}{14}-\dfrac{2}{14}+\dfrac{3}{10}=-1+\dfrac{3}{10}=-\dfrac{7}{10}\)
Ta có: \(\dfrac{-6}{7}+\dfrac{9}{4}\cdot\dfrac{2}{15}-\dfrac{2}{14}\)
\(=\dfrac{-6}{7}-\dfrac{1}{7}+\dfrac{18}{60}\)
\(=-1+\dfrac{3}{10}\)
\(=\dfrac{-10+3}{10}=\dfrac{-7}{10}\)
=(-6/7 - 2/14) + 9/4 * 2/15
=(-6/7 - 1/7) + 3/2 * 1/5
=-1 + 3/10
=-7/10
Sơ đồ thể hiện tác động tiêu cực của việc gia tăng dân số quá nhanh ở đới nóng đối với tài nguyên, môi trường.
1: \(=\dfrac{16}{15}\left(-\dfrac{4}{9}+\dfrac{3}{7}\right)+\dfrac{16}{15}\left(\dfrac{4}{7}-\dfrac{5}{9}\right)\)
\(=\dfrac{16}{15}\left(-\dfrac{4}{9}+\dfrac{3}{7}+\dfrac{4}{7}-\dfrac{5}{9}\right)=0\)
2: \(=\dfrac{29}{9}\left(15+\dfrac{4}{7}-8-\dfrac{1}{7}+\dfrac{15}{7}-\dfrac{1}{7}\right)\)
\(=\dfrac{20}{9}\cdot\left(7\cdot\dfrac{18}{7}\right)=\dfrac{20}{9}\cdot18=40\)
(925 .15 + 925.3) : (926.3- 926)
=925. (15+3) : (926. 3 - 926.1)
=925.18 : 926 .2
=(926 :925) . (18.2)
=9.36
=324
\(\dfrac{9^4.2^{15}}{2^6.24^3}=\dfrac{3^8.2^{15}}{2^6.3^3.2^9}=3^5\)