mình ghi nhầm nên các bạn cứ hết hai phân số là một câu nhé ví dụ như \(\dfrac{-5}{8}\):\(\dfrac{15}{4}\)

a.

4¹⁰ . 8¹⁵ = (2²)¹⁰ . (2³)¹⁵ = 2²⁰ . 2⁴⁵ = 2⁶⁵

b.

4¹⁵ . 5³⁰ = (2²)¹⁵ . 5³⁰ = 2³⁰ . 5³⁰ = (2 . 5)³⁰ = 10³⁰

c.

27¹⁶ : 9¹⁰ = (3³)¹⁶ : (3²)¹⁰ = 3⁴⁸ : 3²⁰ = 3²⁸

Giải:

4¹⁰. 8¹⁵ = (2²)¹⁰ . (2³)¹⁵ = 2²⁰. 2⁴⁵ = 2⁶⁵

4¹⁵. 5³⁰ = (2²)¹⁵. 5³⁰ = 2³⁰. 5³⁰ = (2.5)³⁰ = 10³⁰

27¹⁶ : 9¹⁰ = (3³)¹⁶ : (3²)¹⁰ = 3⁴⁸ : 3²⁰ = 3²⁸

Chúc học tốt nha! ^_^

\(A=\frac{8^{10}+4^{10}}{8^4+4^{11}}\\ =\frac{8^4.8^6+4^{10}}{8^4+4^{10}.4}\\ =\frac{8^6}{4}\\ =\frac{262144}{4}\\ =65536\)

mấy câu sau cứ tương tự

Lời giải:

Ta có:

\(\frac{3}{2^2}.\frac{8}{3^2}.\frac{15}{4^2}....\frac{99}{10^2}=\frac{1.3}{2^2}.\frac{2.4}{3^2}.\frac{3.5}{4^2}...\frac{9.11}{10^2}\)

\(=\frac{(1.3).(2.4).(3.5)...(9.11)}{2^2.3^2.4^2...10^2}\)

\(=\frac{(1.2.3...9)(3.4.5...11)}{(2.3.4...10)(2.3.4..10)}\)

\(=\frac{1}{10}.\frac{11}{2}=\frac{11}{20}\)

\(\dfrac{2}{2^2}.\dfrac{8}{3^2}.\dfrac{15}{4^2}...\dfrac{99}{10^2}\)

=\(\dfrac{1.3}{2.2}.\dfrac{2.4}{3.3}.\dfrac{3.5}{4.4}...\dfrac{9.11}{10.10}\)

=\(\dfrac{1.2.3...9}{2.3.4...10}.\dfrac{3.4.5...11}{2.3.4...10}\)

Rút gọn biểu thức, ta được:

=\(\dfrac{1}{10}\).\(\dfrac{11}{2}\)

=\(\dfrac{11}{22}\)

=\(\dfrac{1}{2}\)

\(goiA=\dfrac{3}{2^2}.\dfrac{8}{3^2}......\dfrac{99}{10^2} \)

\(A=\dfrac{1.3}{2.2}.\dfrac{2.4}{3.3}.......\dfrac{9.11}{10.10}\)

\(A=\dfrac{31}{30}.\dfrac{1}{2}\)

\(A=\dfrac{31}{60}\)

Các bạn ơi,mình ghi thiếu,còn 3 câu nữa nha!!!~~nya

e)| \(\dfrac{5}{2}\)x-\(\dfrac{1}{2}\) |-(-2²).\(\dfrac{1}{3}\)(0,75-\(\dfrac{1}{7}\))=\(\dfrac{-5}{13}\):2\(\dfrac{9}{13}\)-0,5.(\(\dfrac{-2}{3}\))

f)| 5x+21 | = | 2x -63 |

g) -45 - |-3x-96 | - 54=-207

Làm ơn giúp mình với ạ!Mình đang cần gấp lắm trong ngày hôm nay ạ!!!Mình xin cảm ơn các bạn nhiều nhiều lắm luôn đó!!!Thank you very much!!!(^-^)

a, (\(\dfrac{2}{9}\)(6x - \(\dfrac{3}{4}\)) - 3(\(\dfrac{1}{4}x-\dfrac{1}{5}\)) = \(\dfrac{-8}{15}\)

<=> (\(\dfrac{4}{3}x-\dfrac{1}{6}\)) - (\(\dfrac{3}{4}x-\dfrac{3}{5}\)) = \(\dfrac{-8}{15}\)

<=> \(\dfrac{4}{3}x-\dfrac{1}{6}-\dfrac{3}{4}x+\dfrac{3}{5}=\dfrac{-8}{15}\)

<=> \(\dfrac{7}{12}x+\dfrac{13}{30}=\dfrac{-8}{15}\)

<=> \(\dfrac{7}{12}x=\dfrac{-8}{15}-\dfrac{13}{30}\)

<=> \(\dfrac{7}{12}x=-\dfrac{29}{30}\)

<=> x = \(-\dfrac{58}{35}\)
@Nguyễn Gia Hân

a)\(\left(4\frac{5}{37}-3\frac45+8\frac{15}{29}\right)-\left(3\frac{5}{57}-6\frac{14}{29}\right)\)

=\(4\frac{5}{37}-3\frac45+8\frac{15}{29}-3\frac{5}{37}+6\frac{14}{29}\)

=\(\left(4\frac{5}{37}-3\frac{5}{37}\right)+\left(8\frac{15}{29}+6\frac{14}{29}\right)-3\frac45\)

=\(\left\lbrack\left(4-3\right)+\left(\frac{5}{37}-\frac{5}{37}\right)\right\rbrack+\left\lbrack\left(8+6\right)+\left(\frac{15}{29}\right.\right.\)+\(\frac{14}{29})\) -\(\frac{19}{5}\)

=\(1+0+14+1-\frac{19}{5}\)

=\(15+1-\frac{19}{5}\)

=\(16-\frac{19}{5}\)

=\(\frac{80}{5}-\frac{19}{5}\)

=\(\frac{61}{5}\)

A = \(\dfrac{17}{15}.\dfrac{-31}{125}.\dfrac{1}{2}.\dfrac{10}{17}.\dfrac{-1}{8}\)

= \(\dfrac{17.\left(-31\right).1.10.\left(-1\right)}{15.125.2.17.8}\)

= \(\dfrac{17.\left[\left(-31\right).\left(-1\right)\right].1.2.5}{5.3.125.17.4.2}\)

= \(\dfrac{31.1}{3.125.4}\)

= \(\dfrac{31}{1500}\)

B = \(\left(\dfrac{11}{4}.\dfrac{-5}{9}-\dfrac{4}{9}.\dfrac{11}{4}\right).\dfrac{8}{33}\)

= \(\left[\dfrac{11}{4}.\left(\dfrac{-5}{9}-\dfrac{4}{9}\right)\right].\dfrac{8}{33}\)

= \(\left(\dfrac{11}{4}.\dfrac{-9}{9}\right).\dfrac{8}{33}\)

= \(\left[\dfrac{11}{4}.\left(-1\right)\right].\dfrac{4.2}{\left(-11\right).\left(-3\right)}\)

= \(\dfrac{-11}{4}.\dfrac{4.2}{\left(-11\right).\left(-3\right)}\)

= \(\dfrac{\left(-11\right).4.2}{4.\left(-11\right)\left(-3\right)}\)

= \(\dfrac{2}{-3}\)

Ok nhá!

\(a.\)

\(A=\)\(\frac{10^{15}+1}{10^{16}+1}\)

\(10A=\) \(\frac{10\left(10^{15}+1\right)}{10^{16}+1}\)

\(10A=\) \(\frac{10^{16}+10}{10^{16}+1}\)

\(10A=\)\(\frac{10^{16}+1+9}{10^{16}+1}\)

\(10A=\frac{10^{16}+1}{10^{16}+1}+\frac{9}{10^{16}+1}\)

\(10A=1+\frac{9}{10^{16}+1}\)

\(B=\frac{10^{16}+1}{10^{17}+1}\)

\(10B=\frac{10\left(10^{16}+1\right)}{10^{17}+1}\)

\(10B=\frac{10^{17}+10}{10^{17}+1}\)

\(10B=\frac{10^{17}+1+9}{10^{17}+1}\)

\(10B=\frac{10^{17}+1}{10^{17}+1}+\frac{9}{10^{17}+1}\)

\(10B=1+\frac{9}{10^{17}+1}\)

\(\Rightarrow10B< 10A\Rightarrow B< A\)\(\text{( vì tự làm ) }\)

xin lỗi hôm qua mk đang làm thì phải đy học zoom học xong quên h mới nhơ ra làm típ :)

b 

\(A=\frac{3}{8^3}+\frac{7}{8^4}=\frac{3}{8^3}+\frac{3}{8^4}+\frac{4}{8^4}\)

\(B=\frac{3}{8^4}+\frac{7}{8^3}=\frac{3}{8^4}+\frac{3}{8^3}+\frac{4}{8^3}\)

Vì \(\frac{4}{8^4}< \frac{4}{8^3}\)=.> A < B