a,\(x^{16}=x^{12}.x^4\)

\(b,x^{16}=\left(x^4\right)^4\)

\(c,x^{19}:x^3\)

a, \(6.63=9.42\)

\(\Rightarrow\dfrac{6}{9}=\dfrac{42}{63};\dfrac{63}{9}=\dfrac{42}{6};\dfrac{6}{42}=\dfrac{9}{63};\dfrac{63}{42}=\dfrac{9}{6}\)

\(b,0,24.1,61=0,84.0,64\)

\(\Rightarrow\dfrac{0,24}{0,84}=\dfrac{0,64}{1,61};\dfrac{1,61}{0,84}=\dfrac{0,64}{0,24};\dfrac{0,24}{0,64}=\dfrac{0,84}{1,61};\dfrac{1,61}{0,64}=\dfrac{0,84}{0,24}\)

bn có chép sai đề bài ko vậy

bn có chép nhầm đề bài ko vậy

\(a,\dfrac{45^{10}.5^{20}}{75^{15}}=\dfrac{\left(3^2\right)^{10}.5^{10}.5^{20}}{\left(5^2\right)^{15}.3^{15}}=\dfrac{3^{20}.5^{30}}{5^{30}.3^{15}}=3^5=243\)

\(b,\dfrac{\left(0,8\right)^5}{\left(0,4\right)^6}=\dfrac{\left(0,4.2\right)^5}{\left(0.4\right)^6}=\dfrac{\left(0.4\right)^5.2^5}{\left(0,4\right)^6}=\dfrac{2^5}{0,4}=\dfrac{32}{0,4}=80\)

a = \(\frac{n\left(n+1\right)}{2}\); b = 2n + 1

Gọi d = ƯCLN (a; b)

=> a ; b chia hết cho d

a chia hết cho d => 2a chia hết cho d => n(n + 1) chia hết cho d => 2n² + 2n chia hết cho d

b chia hết cho d => 2n + 1 chia hết cho d => 2n² + n chia hết cho d

=> (2n²+ 2n) - (2n² + n) chia hết cho d 

=> n chia hết cho d

Mà 2n + 1 chia hết cho d nên (2n +1) - 2n chia hết cho d => 1 chia hết cho d => d = 1

Vậy a ; b nguyên tố cùng nhau

a, \(\left(\dfrac{2}{3}\right)^3=\dfrac{2^3}{3^3}=\dfrac{8}{27}\)

\(b,\left(-2\dfrac{3}{4}\right)^2=\left(-\dfrac{11}{4}\right)^2=\dfrac{-11^2}{4^2}=\dfrac{121}{16}\)

c,\(\left(0,6\right)^4=\left(\dfrac{6}{10}\right)^4=\left(\dfrac{3}{5}\right)^4=\dfrac{3^4}{5^4}=\dfrac{81}{625}\)

d, \(\left(-\dfrac{1}{2}\right)^4=-\dfrac{1^4}{2^4}=\dfrac{1}{16}\)

e, \(\left(-\dfrac{1}{2}\right)^5=-\dfrac{1^5}{2^5}=-\dfrac{1}{32}\)

a, \(x:\left(\dfrac{3}{4}\right)^3=\left(\dfrac{3}{4}\right)^2\)

\(x=\left(\dfrac{3}{4}\right)^2.\left(\dfrac{3}{4}\right)^3\)

\(x=\left(\dfrac{3}{4}\right)^5\)

b, \(\left(\dfrac{2}{5}\right)^5.x=\left(\dfrac{2}{8}\right)^8\)

\(x=\left(\dfrac{2}{8}\right)^8:\left(\dfrac{2}{5}\right)^5\)

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

\(3,7+\left(-10\right)+4,78+6,3\)

\(=\left(3,7+6,3\right)+\left(-10\right)+4,78\)

\(=10+\left(-10\right)+4,78\)

\(=0+4,78=4,78\)

vô lí !