Rút gọn:
N = \(\frac{9^8.15^{20}}{6^{10}.3^{15}}\)
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1 tháng 8 2018
Ở câu a) số mũ lúc nào cug dương mà bạn ( 45-10 = 4510). Nếu số mũ là dương thì:
a)\(\frac{45^{10}.5^{20}}{75^{15}}\)
= \(\frac{\left(3^2.5\right)^{10}.5^{20}}{\left(3.5^2\right)^{15}}\)
= \(\frac{3^{20}.5^{10}.5^{20}}{3^{15}.5^{30}}\)
= \(\frac{3^{20}.5^{30}}{3^{15}.5^{30}}\)
= \(\frac{3^5.1}{1.1}\)
= \(\frac{243}{1}\)
= 243
b)\(\frac{2^{15}.9^4}{6^6.8^2}\)
= \(\frac{2^{15}.\left(3^2\right)^4}{\left(2.3\right)^6.\left(2^3\right)^2}\)
= \(\frac{2^{15}.3^8}{2^6.3^6.2^6}\)
= \(\frac{2^{15}.3^8}{2^{12}.3^6}\)
= \(\frac{2^3.3^2}{1.1}\)
= \(\frac{8.9}{1}\)
= \(\frac{72}{1}\)
= 72
TT
0
13 tháng 8 2021
\(6\sqrt{\frac{3}{4}}+10\sqrt{\frac{12}{25}}-15\sqrt{\frac{16}{3}}+9\sqrt{\frac{4}{3}}\)
\(=6\cdot\frac{\sqrt{3}}{2}+10\cdot\frac{2\sqrt{3}}{5}-15\cdot\frac{4}{\sqrt{3}}+9\cdot\frac{2}{\sqrt{3}}\)
\(=3\sqrt{3}+4\sqrt{3}-20\sqrt{3}+6\sqrt{3}=-7\sqrt{3}\)
QA
14 tháng 8 2021
Trả lời:
\(6\sqrt{\frac{3}{4}}+10\sqrt{\frac{12}{25}}-15\sqrt{\frac{16}{3}}+9\sqrt{\frac{4}{3}}\)
\(=6.\frac{\sqrt{3}}{\sqrt{4}}+10.\frac{\sqrt{12}}{\sqrt{25}}-15.\frac{\sqrt{16}}{\sqrt{3}}+9.\frac{\sqrt{4}}{\sqrt{3}}\)
\(=6.\frac{\sqrt{3}}{2}+10.\frac{\sqrt{2^2.3}}{5}-15.\frac{4}{\sqrt{3}}+9.\frac{2}{\sqrt{3}}\)
\(=3\sqrt{3}+10.\frac{2\sqrt{3}}{5}-15.\frac{4\sqrt{3}}{3}+9.\frac{2\sqrt{3}}{3}\)
\(=3\sqrt{3}+4\sqrt{3}-20\sqrt{3}+6\sqrt{3}\)
\(=\left(3+4-20+6\right).\sqrt{3}=-7\sqrt{3}\)
\(\frac{9^8.15^{20}}{6^{10}.3^{15}}\)
\(=\frac{\left(3^2\right)^8.\left(3.5\right)^{20}}{\left(2.3\right)^{10}.3^{15}}\)
\(=\frac{3^{16}.3^{20}.5^{20}}{2^{10}.3^{10}.3^{15}}\)
\(=\frac{3^{16+20}.5^{20}}{2^{10}.3^{10+15}}\)
\(=\frac{3^{36}.5^{20}}{2^{10}.3^{25}}\)
\(=\frac{3^{11}.5^{20}}{2^{10}}\)
~Study well~
#Zu
#K bt còn rút gọn đc nx hay k...
N = \(\frac{9^8.15^{20}}{6^{10}.3^{15}}\)
= \(\frac{\left(3^2\right)^8.\left(3.5\right)^{20}}{\left(3.2\right)^{10}.3^{15}}\)
= \(\frac{3^{2.8}.3^{20}.5^{20}}{3^{10}.2^{10}.3^{15}}\)
= \(\frac{3^{16}.3^{20}.5^{20}}{3^{10}.3^{15}.2^{10}}\)
= \(\frac{3^{36}.5^{20}}{3^{25}.2^{10}}\)
= \(\frac{3^{25}.3^{11}.5^{20}}{3^{25}.2^{10}}\)
= \(\frac{3^{11}.5^{20}}{2^{10}}\)