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Ta có :
a) \(\frac{21^{30}}{63^{15}}=\frac{\left(21^2\right)^{15}}{63^{15}}=\left(\frac{21^2}{63}\right)^{15}\)
b) \(\frac{28^9.30^9}{105^9}=\frac{\left(28.30\right)^9}{105^9}=\frac{840^9}{105^9}=\left(\frac{840}{105}\right)^9=8^9\)

\(A=\frac{2^{10}.3^8-2.2^9.3^9}{2^{10}.3^8+2^8.3^8.2^2.5}\)
\(A=\frac{2^{10}.3^8-2^{10}.3^9}{2^{10}.3^8+2^{10}.3^8.5}\)
\(A=\frac{2^{10}.3^8\left(1-3\right)}{2^{10}.3^8\left(1+5\right)}\)
\(A=\frac{1-3}{1+5}\)
\(A=-\frac{1}{3}\)

Mình Gợi Ý Nè
Bạn đưa các cơ số ở cả tử và mẫu về cơ số 2 và 3 rồi đặt các thừa số chung ra ngoài và rút gọn
Mình Ra Kết Quả M = \(\frac{-1}{3}\)
Chúc bạn chăm ngoan học giỏi
và nhớ cho mình tích đậy !

\(=\frac{2^{19}3^9+3\cdot5\cdot2^{18}\cdot3^8}{2^9\cdot3^9\cdot2^{10}+4^{10}\cdot3^{10}}=\frac{2^{19}\cdot3^9+5\cdot2^{18}\cdot3^9}{2^{19}\cdot3^9+2^{20}\cdot3^{10}}=\frac{2^{18}\cdot3^9\cdot\left(2+5\right)}{2^{19}\cdot3^9\left(1+6\right)}=\frac{1}{2}\)

A= -5,13: (\(5\dfrac{5}{28}\)-\(1\dfrac{8}{9}\).1,25+\(1\dfrac{16}{63}\))
A=-5,13:(\(\dfrac{145}{28}\)-\(\dfrac{17}{9}\). 1,25+\(\dfrac{79}{63}\))
A= -5,13:(\(\dfrac{145}{28}\)-\(\dfrac{85}{36}\)+ \(\dfrac{79}{63}\))
A= -5,13:\(\dfrac{57}{14}\)
A= -\(\dfrac{63}{50}\)

a) \(A=-5,13:\left(5\dfrac{5}{28}-1\dfrac{8}{9}.1,25+1\dfrac{16}{63}\right)\)
\(\Leftrightarrow A=-5,13:\left(5\dfrac{5}{28}-\dfrac{85}{36}+1\dfrac{16}{63}\right)\)
\(\Leftrightarrow A=-5,13:\left(\dfrac{355}{126}+1\dfrac{16}{63}\right)\)
\(\Leftrightarrow A=-5,13:\dfrac{57}{14}\)
\(\Leftrightarrow A=\dfrac{-63}{50}\)
b) \(B=\left(3\dfrac{1}{3}.1,9+19,5:4\dfrac{1}{3}\right).\left(\dfrac{62}{75}-\dfrac{4}{25}\right)\)
\(\Leftrightarrow B=\left(\dfrac{19}{3}+19,5.\dfrac{3}{13}\right).\dfrac{2}{3}\)
\(\Leftrightarrow B=\left(\dfrac{19}{3}+\dfrac{9}{2}\right).\dfrac{2}{3}\)
\(\Leftrightarrow B=\dfrac{65}{6}.\dfrac{2}{3}\)
\(\Leftrightarrow B=\dfrac{65}{9}\)

=\(\frac{7^{15}.2^{30}.3^{17}}{7^{16}.3^{16}.2^{32}}\)=\(\frac{3}{7.3.2^2}\)=\(\frac{1}{7.2^2}\)=\(\frac{1}{28}\)

So sánh: 7215 và 321.969
7215=(23.32)15=(23)15.(32)15=245.330
321.969=321.(3.25)9=321.39.(25)9=321+9.245=330.245
Vì 245.330 = 3030.245
Nên 7215 = 321.969

=\(\dfrac{\left(\dfrac{7}{2^9}-\dfrac{14}{2^{11}}+\dfrac{21}{768}\right)^2}{\left(\dfrac{5}{2^9}-\dfrac{20}{2^{12}}+\dfrac{25}{1280}\right)^2}\)
= \(\dfrac{\left[7.\left(\dfrac{1}{2^9}-\dfrac{2}{2^{11}}+\dfrac{3}{768}\right)\right]^2}{\left[5.\left(\dfrac{1}{2^9}-\dfrac{4}{2^{12}}+\dfrac{5}{1280}\right)\right]^2}\)
=\(\dfrac{7^2}{5^2}\)
\(\dfrac{28^9.30^9}{105^9}=\left(\dfrac{4.7.15.2}{105}\right)^9=\left(\dfrac{4.105.2}{105}\right)^9=8^9\)