a,\(\left(\dfrac{3}{7}+\dfrac{1}{2}\right)^2\)

\(=\left(\dfrac{13}{14}\right)^2\)

\(=\dfrac{169}{196}\)

b,\(\left(\dfrac{3}{4}-\dfrac{5}{6}\right)^2\)

\(=\left(\dfrac{-1}{12}\right)^2\)

\(=\dfrac{1}{144}\)

c,\(\dfrac{5^4.20^4}{25^5.4^5}\)

\(=\dfrac{100^4}{100^5}\)

\(=\dfrac{1}{100}\)

d,\(\left(\dfrac{-10}{3}\right)^5.\left(\dfrac{-6}{5}\right)^4\)

\(=\left(\dfrac{-10}{3}\right)^4.\left(\dfrac{-6}{5}\right)^4.\left(\dfrac{-10}{3}\right)\)

\(=\left(\dfrac{\left(-10\right)}{3}.\dfrac{\left(-6\right)}{5}\right)^4.\left(\dfrac{-10}{3}\right)\)

\(=4^4.\left(\dfrac{-10}{3}\right)\)

\(=256.\left(\dfrac{-10}{3}\right)\)

\(=\dfrac{-2560}{3}\)

a.\(\left(\frac{3}{7}+\frac{1}{2}\right)^2\)

=\(\left(\frac{6}{14}+\frac{7}{14}\right)^2\)

=\(\left(\frac{13}{14}\right)^2\)

=\(\frac{13^2}{14^2}\)

=\(\frac{169}{196}\)

b.\(\left(\frac{3}{4}-\frac{5}{6}\right)^2\)

=\(\left(\frac{9}{12}-\frac{10}{12}\right)^2\)

=\(\left(\frac{-1}{12}\right)^2\)

=\(\frac{-1^2}{12^2}\)

=\(\frac{1}{144}\).

c.Phần C bn viết lại đề bài đi,mk ko hiểu

d.\(\left(\frac{-10}{3}\right)^5.\left(\frac{-6}{5}\right)^4\)

=\(\frac{-10^5}{3^5}.\left(\frac{-6^4}{5^4}\right)\)

=\(\frac{-100000}{243}.\frac{1296}{625}\)

=\(\frac{-2560}{3}\)

                 Không biết đúng ko nữa

c.\(\frac{5^4.20^4}{25^5.4^5}\)

=\(\frac{25^2.\left(5.4\right)^4}{25^5.4^5}\)

=\(\frac{1.\left(5\right)^4.\left(4\right)^4}{25^3.4^5}\)

=\(\frac{25^2.1}{25^3.4}\)

=\(\frac{1}{25.4}\)

=\(\frac{1}{100}\).

Đề bài phần c là thế này ak Nguyễn Bình Minh:

\(\frac{5^4.20^4}{25^5.4^5}\) ak??

Bài 1: 

a) 0²⁰⁰² < 0²⁰²³

b) 2022⁰ = 2023⁰

c) 54⁹ < 55¹⁰

d) ( 4 + 5 )³ > 4² + 5²

đ) 9² - 3² > ( 9 - 3 )²

Bài 2:

a) 3² x 4³ - 3² + 333

= 9 x 64 - 9 + 333

= 576 - 9 + 333

= 567 + 333

= 900

b) 5 x 4³ + 24 x 5 + 41⁰

= 5 x 64 + 24 x 5 + 1

= 5 x ( 64 + 24 ) + 1

= 5 x 88 + 1

= 440 + 1

= 441

c) 2³ x 4² + 3² x 5 - 40 x 1²⁰²³

= 8 x 16 + 9 x 5 - 40 x 1

= 128 + 45 - 40

= 133

Bài 1 :

a) \(0^{2002}=0;0^{2023}=0\Rightarrow0^{2002}=0^{2023}\)

b) \(2022^0=1;2023^0=1\Rightarrow2022^0=2023^0\)

c) \(54^9< 55^9;55^9< 55^{10}\Rightarrow54^9< 55^{10}\)

d) \(\left(4+5\right)^3>\left(4+5\right)^2;\left(4+5\right)^2>4^2+5^2\Rightarrow\left(4+5\right)^3>4^2+5^2\)

đ) \(9^2-3^2=81-9=82;\left(9-3\right)^2=6^2=36\Rightarrow9^2-3^2>\left(9-3\right)^2\)

Bài 2 :

a) \(3^2.4^3-3^2+333=3^2\left(4^3-1\right)+9.37=9.63+9.37=9\left(63+37\right)=9.100=900\)

b) \(5.4^3+24.5+41^0=20.4^2+20.6+1=20\left(16+6\right)+1=20.22+1=441\)

c) \(2^3.4^2+3^2.5-40.1^{2023}=8.16+9.5-40.1=128+45-40=128+5=133\)

a) \(9.3^3.\frac{1}{81}.3^2=3^2.3^3.\frac{1}{3^4}.3^2=3^7.\frac{1}{3^4}=3^3\)

b) \(4.2^5:\left(2^3.\frac{1}{16}\right)=2^2.2^5:2^3:\frac{1}{16}=2^7:2^3.16=2^4.2^4=2^8\)

c) \(3^2.2^5.\left(\frac{2}{3}\right)^2=3^2.2^5.\frac{2^2}{3^2}=2^5.2^2=2^7\)

d) \(\left(\frac{1}{3}\right)^2.\frac{1}{3}.9^2=\left(\frac{1}{3}\right)^3.\left(3^2\right)^2=\frac{1^3}{3^3}.3^4=1^3.3=3^1\)

a.\(\left(1+\frac{2}{3}-\frac{1}{4}\right).\left(\frac{4}{5}-\frac{3}{4}\right)^2\)

=\(\left(\frac{12}{12}+\frac{8}{12}-\frac{3}{12}\right).\left(\frac{16}{20}-\frac{15}{20}\right)^2\)

=\(\frac{17}{12}.\left(\frac{1}{20}\right)^2\)

=\(\frac{17}{12}.\frac{1}{400}\).

=\(\frac{17}{4800}\)

b.\(2:\left(\frac{1}{2}-\frac{2}{3}\right)^3\)

=\(2:\left(\frac{3}{6}-\frac{4}{6}\right)^3\)

=\(2:\left(\frac{-1}{6}\right)^3\)

=\(2:\left(\frac{-1}{216}\right)\)

=\(\frac{-216.2}{1}\)

=-432.

Ai trả lời được câu này sẽ được mình tíc cho nhé !!!

Ai trả lời được câu này thì mình tíc cho nha !!!

a) \(\frac{16}{2^n}=2\)

=> 2.2ⁿ = 16

=> 2¹⁺ⁿ = 2⁴

=> 1 + n = 4

=> n = 4 - 1

=> n = 3

Vậy n = 3

b) \(\frac{\left(-3\right)^n}{81}=-27\)

=> (-3)ⁿ = -27.81

=> (-3)ⁿ = -3³.3⁴

=> (-3)ⁿ = (-3)⁷

=> n = 7

Vậy n = 7

c) 8ⁿ : 2ⁿ = 4

=> (8 : 2)ⁿ = 4

=> 4ⁿ = 4¹

=> n = 1

Vậy n = 1

a: \(\Leftrightarrow2^5\ge2^n>2^2\)

=>2<n<=5

hay \(n\in\left\{3;4;5\right\}\)

b: \(\Leftrightarrow3^2\cdot3^3\le3^n\le3^5\)

=>5<=n<=5

=>n=5

Ta có:

\(8^7-2^{18}=8^7-\left(2^3\right)^6=8^7-8^6=8^5.\left(8^2-8\right)=8^5.56⋮14\)

\(\Rightarrow8^7-2^{18}⋮14\left(đpcm\right)\)

\(8^7-2^{18}=\left(2^3\right)^7-2^{18}=2^{21}-2^{18}=2^{18}.2^3-2^{18}=2^{18}\left(2^3-1\right)=2^{18}.7=2^{17}.2.7=2^{17}.14⋮14\)

Vây....................