ý B hình như mk giải rồi thì phải

\(A=\frac{a^2.a^7.b^2.c^8}{a^5.b^3.\left(-c\right)^4}=\frac{a^9.b^2.c^8}{a^5.b^3.c^4}=\frac{a^4.c^4}{b}\)

\(B=\left(\frac{3}{7}\right)^5.\frac{\left(25\right)^4.7^5}{15^4.20^2}=\frac{3^5.\left(5^2\right)^4.7^5}{7^5.\left(3.5\right)^4.\left(4.5\right)^2}=\frac{3^5.5^8.7^5}{7^5.3^4.5^4.4^2.5^2}\)

    \(=\frac{3^5.5^8.7^5}{7^5.3^4.5^6.4^2}=\frac{3.5^2}{4^2}=\frac{75}{16}\)

P ơi là Rút gọn mk quên k ghi đề bài

Bài làm

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

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

\(=\frac{9}{49}+\frac{1}{4}\)

\(=\frac{36}{196}+\frac{49}{196}\)

\(=\frac{85}{196}\)

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

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

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

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

\(=\frac{5^4.\left(5.4\right)^4}{\left(5.5\right)^5.4^5}\)

\(=\frac{5^4.5^4.4^4}{5^5.5^5.4^5}\)

\(=\frac{1}{5.5.4}\)

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

~ Check đúng cho minh nha. ~

# Học tốt #

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

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

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

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

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

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

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

\(< =>\frac{-1}{144}\)

\(c,\frac{5^4\cdot20^4}{25^5\cdot4^5}\)

\(< =>\frac{25^2\cdot\left(4\right)^4\cdot\left(5\right)^4}{25^5\cdot4^5}\)

\(< =>\frac{1\cdot1\cdot\left(5\right)^4}{25^3\cdot4}\)

\(< =>\frac{1\cdot25^2}{25^3\cdot4}\)

\(< =>\frac{1}{25\cdot4}\)

\(< =>\frac{1}{100}\)

a,(3/7)^2+2.3/7.1/2+(1/2)^2

=9/49+3/7+1/4

=169/196

b,(3/4)^2-2.3/4.5/6+(5/6)^2

=9/16-5/4+25/36

=1/144

a) \(\left(\frac{3}{7}+\frac{1}{2}\right)^2=\left(\frac{6}{14}+\frac{7}{14}\right)^2=\left(\frac{13}{14}\right)^2=\frac{169}{196}\)

b) \(\left(\frac{3}{4}-\frac{5}{6}\right)^2=\left(\frac{9}{12}-\frac{10}{12}\right)^2=\left(-\frac{1}{2}\right)^2=\frac{1}{4}\)
d) \(\left(-\frac{10}{3}\right)^5.\left(-\frac{6}{5}\right)^4=-\frac{2560}{3}\)
e) \(\left(1+\frac{2}{3}-\frac{1}{4}\right).\left(\frac{4}{5}-\frac{3}{4}\right)^2=\frac{17}{12}.\left(\frac{1}{20}\right)^2=\frac{17}{12}.\frac{1}{400}=\frac{17}{4800}\)

f) \(2:\left(\frac{1}{2}-\frac{2}{3}\right)^3=2:\left(-\frac{1}{6}\right)^3=2:-\frac{1}{216}=-432\)

a)  Ta có : 

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

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

= \(\left(\frac{13}{14}\right)^2\)

= \(\frac{169}{196}\)

b)

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

= \(\left(\frac{18}{24}-\frac{20}{24}\right)^2\)

= \(\left(\frac{-1}{12}\right)^2\)

= \(\frac{1}{144}\)

f) \(\frac{3^3.\left(0,5\right)^5}{\left(1,5\right)^4}=\frac{3^3.\left(0,5\right)^5}{\left[3.\left(0,5\right)\right]^4}=\frac{3^3.\left(0,5\right)^5}{3^4.\left(0,5\right)^4}=\frac{0,5}{3}=\frac{1}{6}\)

b) \(\frac{2^3+3.2^6-4^3}{2^3+3^2}=\frac{2^3.\left(1+3.2^3-2^3\right)}{2^3+3^2}=\frac{2^3.17}{17}=2^3=8\)

Các phần còn lại tương tự, bạn tự làm nhé !

(*) Lưu ý ở những bài rút gọn có chứa lũy thừa thì bạn đưa số đó về số nguyên tố rồi thực hiện như bình thường .

VD : \(4^3=\left(2^2\right)^3=2^6\) ( đưa về số nguyên tố là 2 )

\(6^3=\left(2.3\right)^3=2^3.3^3\) ( đưa về tích hai số nguyên tố )

a, \(\frac{169}{196}\)

b, \(\frac{1}{144}\)

c, \(\frac{1}{100}\)

d, \(\frac{-2560}{3}\)

\(\left(\frac{3}{7}+\frac{1}{2}\right)^2=\left(\frac{13}{14}\right)^2=\frac{169}{196}\)

\(\left(\frac{3}{4}-\frac{5}{6}\right)^2=\left(-\frac{1}{12}\right)^2=\frac{1}{144}\)

\(\frac{5^4.20^4}{25^5.4^5}=\frac{5^8.2^8}{5^{10}.42^{10}}=\frac{1}{100}\)

\(\left(-\frac{10}{3}\right)^5.\left(-\frac{6}{5}\right)^4=\left[\left(-\frac{10}{3}\right).\left(-\frac{6}{5}\right)\right]^4.\left(-\frac{10}{3}\right)=4^4.\left(-\frac{10}{3}\right)=-\frac{2560}{3}\)

a. \(\left(\frac{3}{7}+\frac{1}{2}\right)^2=\left(\frac{6+7}{14}\right)^2=\left(\frac{13}{14}\right)^2=\frac{13^2}{14^2}=\frac{169}{196}\)

b. \(\left(\frac{3}{4}-\frac{5}{6}\right)^2=\left(\frac{9-10}{12}\right)^2=\left(-\frac{1}{12}\right)^2=\frac{\left(-1\right)^2}{12^2}=\frac{1}{144}\)

c. \(\frac{5^4.20^4}{25^5.4^5}=\frac{\left(5.20\right)^4}{\left(25.4\right)^5}=\frac{100^4}{100^5}=\frac{1}{100}\)

d.\(\left(-\frac{10}{3}\right)^5.\left(-\frac{6}{5}\right)^4=\frac{\left(-10\right)^5}{3^5}.\frac{\left(-6\right)^4}{5^4}=\frac{\left(-2.5\right)^5.\left(-2.3\right)^4}{3^5.5^4}=\frac{\left(-2\right)^5.5^5.\left(-2\right)^4.3^4}{3^5.5^4}=\frac{\left(-2\right)^9.5}{3}=\frac{-512.5}{3}=-\frac{2560}{3}\)