\(\dfrac{9^4.2^{15}}{2^6.24^3}\) = \(\dfrac{9^4.2^9}{24^3}\) = \(\dfrac{2^9.3^8}{2^9.3^3}\) = 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

Giải:

6/-7+9/4.2/15-2/14

=-6/7+3/10-2/14

=(-6/7-2/14)+3/10

=-1+3/10

=-7/10

Chúc bạn học tốt!

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: \(=\dfrac{29}{9}\left(15+\dfrac{4}{7}-8-\dfrac{1}{7}+\dfrac{15}{7}-\dfrac{1}{7}\right)\)

\(=\dfrac{20}{9}\cdot\left(7\cdot\dfrac{18}{7}\right)=\dfrac{20}{9}\cdot18=40\)

(9^{25 .}15 + 9²⁵.3) : (9²⁶.3- 9²⁶⁾

=9²⁵. (15+3) : (9²⁶. 3 - 9²⁶.1)

=9²⁵.18 : 9²⁶ .2

=(9²⁶ :9²⁵) . (18.2)

=9.36

=324

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