Ta có: \(\frac{2^{12}\cdot3^5-4^6\cdot9^2}{\left(2^2\cdot3\right)^6}\)

\(=\frac{2^{12}\cdot3^5-2^{12}\cdot3^4}{2^{12}\cdot3^6}=\frac{2^{12}\cdot3^4\left(3-1\right)}{2^{12}\cdot3^6}\)

\(=\frac{3^4\cdot2}{3^6}=\frac{2}{3^2}=\frac29\)

Ta có: \(\frac{5^{10}\cdot7^3-25^5\cdot49^2}{\left(125\cdot7\right)^3+5^9\cdot14^3}\)

\(=\frac{5^{10}\cdot7^3-5^{10}\cdot7^4}{5^9\cdot7^3+5^9\cdot7^3\cdot2^3}\)

\(=\frac{5^{10}\cdot7^3\left(1-7\right)}{5^9\cdot7^3\left(1+2^3\right)}=5\cdot\frac{-6}{9}=5\cdot\frac{-2}{3}=-\frac{10}{3}\)

Ta có: \(A=\frac{2^{12}\cdot3^5-4^6\cdot9^2}{\left(2^2\cdot3\right)^6}-\frac{5^{10}\cdot7^3-25^5\cdot49^2}{\left(125\cdot7\right)^3+5^9\cdot14^3}\)

\(=\frac29+\frac{10}{3}=\frac29+\frac{30}{9}=\frac{32}{9}\)

Các bạn giúp mk với, nhanh nhé, mk cần gấp

Câu a có 1 số 0 to thôi nhé!

@@

là sao bạn

\(\left(\dfrac{3}{5}\right)^5.x=\left(\dfrac{9}{25}\right)^3.\left(\dfrac{3}{5}\right)^2\)

\(\Rightarrow\left(\dfrac{3}{5}\right)^3.x=\left(\dfrac{9}{25}\right)^3\)

\(\Rightarrow x=\left(\dfrac{3}{5}\right)^3\)

\(\Rightarrow x=\dfrac{27}{125}\)

Bạn sai rồi nhé như thế này mới đúng :

Lời giải :

\(\left(\dfrac{3}{5}\right)^5.x=\left(\dfrac{9}{25}\right)^3.\left(\dfrac{3}{5}\right)^2\)

\(\left(\dfrac{3}{5}\right)^2.\left(\dfrac{3}{5}\right)^3.x=\left(\dfrac{9}{25}\right)^3.\left(\dfrac{3}{5}\right)^2\)

Vì : \(\left(\dfrac{3}{5}\right)^2=\left(\dfrac{3}{5}\right)^2\)

Nên : \(\left(\dfrac{3}{5}\right)^3.x=\left(\dfrac{9}{25}\right)^3\)

\(\Rightarrow x=\left(\dfrac{9}{25}\right)^3:\left(\dfrac{3}{5}\right)^3\)

\(\Rightarrow x=\left(\dfrac{9}{25}:\dfrac{3}{5}\right)^3\)

\(\Rightarrow x=\left(\dfrac{3}{5}\right)^3\)

\(\Rightarrow x=\dfrac{3.3.3}{5.5.5}\)

\(\Rightarrow x=\dfrac{3^3}{5^3}\)

\(\Rightarrow x=\left(3:5\right)^3\)

\(\Rightarrow x=0,6^3\)

\(\Rightarrow x=0,216\)

Vậy \(x=0,216\)

không vt lại đề

\(=\frac{2^{12}.3^5-2^{12}.3^4}{2^{12}.3^6+2^{12}.3^5}-\frac{5^{10}.7^3-5^{10}.7^4}{5^6.7^3+5^9.2^3.7^3}\)

\(=\frac{2^{12}\cdot3^4.\left(3-1\right)}{2^{12}.3^5.\left(3+1\right)}-\frac{5^{10}.7^3\left(1-7\right)}{5^6.7^3\left(1+2^3\right)}\)

\(=\frac{1}{6}-\frac{-10}{3}=\frac{1}{6}+\frac{20}{6}=\frac{21}{6}\)

bạn chưa rút gọn 

\(B=\frac{2^{13}.3^5-4^6.9^2}{\left(2^2.3\right)^6+8^4.3^5}-\frac{5^{10}.7^3-25^5.49^2}{\left(125.7\right)^3+5^9.14^3}\)

\(=\frac{2^{13}.3^5-\left(2^2\right)^6.\left(3^2\right)^2}{2^{12}.3^6+\left(2^3\right)^4.3^5}-\frac{5^{10}.7^3-\left(5^2\right)^5.\left(7^2\right)^2}{\left(5^3.7\right)^3+5^9.\left(2.7\right)^3}\)

\(=\frac{2^{13}.3^5-2^{12}.3^4}{2^{12}.3^6+2^{12}.3^5}-\frac{5^{10}.7^3-5^{10}.7^4}{5^9.7^3+5^9.2^3.7^3}\)

\(=\frac{2^{12}.3^4\left(2.3-1\right)}{2^{12}.3^5\left(3+1\right)}-\frac{5^{10}.7^3\left(1-7\right)}{5^9.7^3.\left(1+2^3\right)}\)

\(=\frac{2^{12}.3^4.5}{2^{12}.3^5.4}-\frac{5^{10}.7^3.\left(-6\right)}{5^9.7^3.9}\)

\(=\frac{5}{12}-\frac{-10}{3}=\frac{5}{12}+\frac{40}{12}=\frac{45}{12}=\frac{15}{4}=3\frac{3}{4}\)

\(=\dfrac{2^{12}\cdot3^5-2^{12}\cdot3^4}{2^{18}\cdot3^6+2^{12}\cdot3^5}-\dfrac{5^{10}\cdot7^3-5^{10}\cdot7^4}{5^9\cdot7^3+5^9\cdot2^3\cdot7^3}\)

\(=\dfrac{2^{12}\cdot3^4\cdot2}{2^{12}\cdot3^5\left(2^6\cdot3+1\right)}-\dfrac{5^{10}\cdot7^3\cdot\left(-6\right)}{5^9\cdot7^3\cdot9}\)

\(=\dfrac{2}{193}+\dfrac{5\cdot2}{3}=\dfrac{1936}{579}\)

Giups mình với !

Mai mình phải nộp rồi >o<

a) 25 + 3x = 25 - 1

3x = -1

x = -1/3

b) (6x-39):13 = 201

6x-39 = 2613

6x = 2652

x = 442

c) 2^x + 3⁵:3⁴ = 5¹⁰ : 5⁸

2^x + 3 = 25

2^x = 22

...

a)\(\dfrac{6^2.6^3}{3^5}=\dfrac{2^2.3^2.2^3.3^3}{3^5}=2^5=32\)

b)\(\dfrac{25^2.4^2}{5^5\left(-2\right)^5}=\dfrac{5^2.5^2.2^2.2^2}{5^5.\left(-2\right)^5}=\dfrac{1}{-10}=-\dfrac{1}{10}\)

c)\(\dfrac{2^7.9^3}{8^2.3^6}=\dfrac{2^7.\left(3^2\right)^3}{\left(2^3\right)^2.3^6}=\dfrac{2^7.3^6}{2^6.3^6}=2\)

d)\(\dfrac{6^3+3.6^2+3^3}{-13}=\dfrac{2^3.3^3+3.2^2.3^2+3^3}{-13}=\dfrac{3^3\left(2^3+2^2+1\right)}{-13}\)

\(=\dfrac{3^3.13}{-13}=-3^3=-27\)