Rút gọn phấn số
\(\frac{3^{10}.\left(-5\right).21}{\left(-5\right)^{20}.3^{12}}\)
Giúp mình vs
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\(\frac{3^{10}.\left(-5\right)^{21}}{\left(-5\right)^{20}.3^{12}}=\frac{3^{10}.\left(-5\right)^{20}.\left(-5\right)}{\left(-5\right)^{20}.3^{10}.3^2}=\frac{-5}{3^2}=-\frac{5}{9}\)
\(\frac{3^{10}.\left(-5\right)^{21}}{\left(-5\right)^{20}.3^{12}}=\frac{3^{10}.\left(-5\right)^{20}.\left(-5\right)}{\left(-5\right)^{20}.3^{10}.3^2}=\frac{-5}{3^2}=\frac{-5}{9}\)
\(\frac{3^{10}.\left(-5\right)^{21}}{\left(-5\right)^{20}.3^{12}}=\frac{1.\left(-5\right)}{1.3^2}=-\frac{5}{9}\)
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Giari thích :
\(3^{12}:3^{10}=3^{12-10}=3^2=9\)
\(\left(-5\right)^{21}:\left(-5\right)^{20}=\left(-5\right)^{21-20}=\left(-5\right)^1=\left(-5\right)\)
\(\frac{3^{10}.\left(-5\right)^{21}}{\left(-5\right)^{20}.3^{12}}\)
\(=\frac{\left(-5\right)}{3^2}\)
\(=\frac{-5}{9}\)
OK
Hai câu a) và b) bạn chỉ cần xem số mũ rồi trừ số mũ là xong
\(c)\) \(\frac{2^{10}.3^{10}-2^{10}.3^9}{2^9.3^{10}}=\frac{2^{10}.3^9\left(3-1\right)}{2^9.3^{10}}=\frac{2^{10}.3^9.2}{2^9.3^{10}}=\frac{2^{11}.3^9}{2^9.3^{10}}=\frac{2^2}{3}=\frac{4}{3}\)
\(d)\) \(\frac{5^{11}.7^{12}+5^{11}.7^{11}}{5^{12}.7^{12}+9.5^{11}.7^{11}}=\frac{5^{11}.7^{11}\left(7+1\right)}{5^{11}.7^{11}\left(5.7+9\right)}=\frac{8}{35+9}=\frac{8}{44}=\frac{2}{11}\)
Chúc bạn học tốt
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\(A=\left(\sqrt{5}+2\right)\frac{5+4\sqrt{5}+4-8\sqrt{5}}{\sqrt{5}-2}\\ A=\left(\sqrt{5}+2\right)\frac{5-4\sqrt{5}+4}{\sqrt{5}-2}\\ A=\left(\sqrt{5}+2\right)\frac{\left(\sqrt{5}-2\right)^2}{\sqrt{5}-2}\\ A=\left(\sqrt{5}+2\right)\left(\sqrt{5}-2\right)\\ A=1\)
Ta có:\(\frac{3^{10}\cdot\left(-5\right)\cdot21}{\left(-5\right)^{20}\cdot3^{12}}\)
\(=\frac{3^{10}\cdot\left(-5\right)\cdot21}{\left(-5\right)^{19}\cdot\left(-5\right)\cdot3^{12}}\)
\(=\frac{3\cdot7}{\left(-5\right)^{19}\cdot3^2}\)
\(=\frac{7}{\left(-5\right)^{19}\cdot3}\)