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\(\frac{45^{10}\times5^{20}}{75^{15}}=\frac{3^{20}\times5^{10}\times5^{20}}{3^{15}\times5^{30}}=3^5=243\)
ta có \(\frac{45^{10}.5^{20}}{75^{15}}=\frac{\left(3^2.5\right)^{10}.5^{20}}{\left(5^2.3\right)^{15}}=\frac{3^{20}.5^{10}.5^{20}}{5^{30}.3^{15}}=3^5=243\)
hậu quả của việc chép sai đề là đây : mỏi tay , nhức óc , lại còn k đc ****
a.
\(\frac{45^{10}\times5^{20}}{75^{15}}=\frac{\left(3^2\times5\right)^{10}\times5^{20}}{\left(3\times5^2\right)^{15}}=\frac{3^{20}\times5^{10}\times5^{20}}{3^{15}\times5^{30}}=3^5=243\)
b.
\(\frac{\left(0,8\right)^5}{\left(0,4\right)^6}=\frac{\left(0,8\right)^5}{\left(0,4\right)^5}\times\frac{1}{\left(0,4\right)}=\left(\frac{0,8}{0,4}\right)^5\times\frac{1}{\frac{4}{10}}=2^5\times\frac{5}{2}=2^4\times5=16\times5=80\)
c.
\(\frac{2^{15}\times9^4}{6^6\times8^3}=\frac{2^{15}\times\left(3^2\right)^4}{\left(2\times3\right)^6\times\left(2^3\right)^3}=\frac{2^{15}\times3^8}{2^6\times3^6\times2^9}=3^2=9\)
Chúc bạn học tốt ^^
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a) \(\frac{45^{10}\times5^{20}}{75^{15}}\)
\(=\frac{\left(15\times3\right)^{10}\times5^{20}}{\left(15\times5\right)^{15}}\)
\(=\frac{15^{10}\times3^{10}\times5^{20}}{15^{15}\times5^{15}}\)
\(=\frac{1\times3^{10}\times5^5}{15^5\times1}\)
\(=\frac{3^{10}\times5^5}{\left(3\times5\right)^5}\)
\(=\frac{3^{10}\times5^5}{3^5\times5^5}\)
\(=3^5=243\)
\(\frac{45^{10}.5^{20}}{75^{15}}\)
\(=\frac{5.3^{20}.5^{20}}{\left(5^2.3\right)^{15}}=\frac{5^{21}.3^{20}}{5^{30}.3^{15}}=\frac{5^{21}.3^{15}.3^5}{5^{21}.5^9.3^{15}}=\frac{3^5}{5^9}\).
\(\frac{45^{10}.5^{20}}{75^{15}}=\frac{\left(9.5\right)^{10}.5^{20}}{\left(3.25\right)^{15}}\)
\(=\frac{9^{10}.5^{10}.5^{20}}{3^{15}.25^{15}}\)
\(=\frac{\left(3^2\right)^{10}.5^{10}.5^{20}}{3^{15}.\left(5^2\right)^{15}}\)
\(=\frac{3^{20}.5^{30}}{3^{15}.5^{30}}\)
\(=\frac{3^{20}}{3^{15}}\)
\(=3^5\)
\(=243\)
\(\frac{45^{10}.5^{20}}{75^{15}}\)
\(=\frac{\left(15.3\right)^{10}.5^{20}}{\left(15.5\right)^{15}}\)
\(=\frac{15^{10}.3^{10}.5^{20}}{15^{15}.5^{15}}\)
\(=\frac{3^{10}.5^5}{15^5}=\frac{3^{10}.5^5}{3^5.5^5}=3^5=243\)
\(\frac{45^{10}.5^{20}}{75^{15}}=\frac{\left(9.5\right)^{10}.5^{20}}{\left(3.5.5\right)^{15}}=\frac{9^{10}.5^{10}.5^{20}}{3^{15}.5^{15}.5^{15}}=\frac{9^{10}.5^{30}}{3^{15}.5^{30}}=\frac{9^{10}}{3^{15}}=243\)
a) A = \(\frac{45^{10}.5^{10}}{75^{10}}=\frac{\left(5.3^2\right)^{10}.5^{10}}{\left(5^2.3\right)^{10}}=\frac{5^{10}.3^{20}.5^{10}}{5^{20}.3^{10}}=\frac{5^{20}.3^{10}}{5^{20}}=3^{10}=59049\)
b) B = \(\frac{\left(0,8\right)^5}{\left(0,4\right)^6}=\frac{\left(0,2.2^2\right)^5}{\left(0,2.2\right)^6}=\frac{\left(0,2\right)^5.2^{10}}{\left(0,2\right)^6.2^6}=\frac{2^4}{0,2}=\frac{16}{0,2}=80\)
c) C = \(\frac{2^{15}.9^4}{6^6.8^3}=\frac{2^{15}.\left(3^2\right)^4}{\left(2.3\right)^6.\left(2^3\right)^3}=\frac{2^{15}.3^8}{2^6.3^6.2^9}=\frac{2^{15}.3^2}{2^{15}}=3^2=9\)
\(A=\frac{\left(9^{10}×5^{10}×5^{10}\right)}{\left(25^{10}×3^{10}\right)}\)
\(A=\frac{\left(3^{20}×5^{20}\right)}{\left(5^{20}×3^{10}\right)}\)
\(A=\frac{3^{20}}{3^{10}}\)
\(A=3^{10}\)
a) \(\frac{45^{10}.5^{20}}{75^{15}}\)
=
\(\frac{\left(5.9\right)^{10}.5^{20}}{\left(5.15\right)^{15}}\)
= \(\frac{5^{10}.9^{10}.5^{20}}{5^{15}.15^{15}}\)
= \(\frac{5^{10}.3^{20}.5^{20}}{5^{15}.15^{15}}\)
= \(\frac{5^{10}.15^{20}}{5^{15}.15^{15}}\)
= \(\frac{15^5}{5^5}\)
= \(\frac{3^5.5^5}{5^5}\)
= \(3^5\)
b) \(\frac{\left(0,8\right)^5}{\left(0,4\right)^6}\)
= \(\frac{\left(0,4\right)^5.2^5}{\left(0,4\right)^6}\)
= \(\frac{2^5}{0,4}\)
= \(2^5\) : 0,4
(=) 32 : \(\frac{2}{5}\)
= 90
c) \(\frac{2^{15}.9^4}{6^6.8^3}\)
= \(\frac{2^{15}.\left(3^2\right)^4}{\left(2.3\right)^6.\left(2^3\right)^3}\)
= \(\frac{2^{15}.3^8}{2^6.3^6.2^9}\)
= \(3^2\)
\(=\frac{\left(3\cdot3\cdot5\right)^{10}\cdot5^{20}}{\left(3\cdot5\cdot5\right)^{15}}\)
\(=\frac{3^{10}\cdot3^{10}\cdot5^{10}\cdot5^{20}}{3^{15}\cdot5^{15}\cdot5^{15}}\)
\(=\frac{3^{20}\cdot5^{30}}{3^{15}\cdot5^{30}}\)
\(=3^5=243\)
nhớ nha