\(A=\frac{45^{10}.5^{10}}{75^5}\)
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\(\frac{45^{10}.5^{10}}{75^{40}}=\frac{\left(5.3^2\right)^{10}.5^{10}}{\left(5^2.3\right)^{40}}=\frac{5^{10}.3^{20}.5^{10}}{5^{80}.3^{40}}=\frac{1}{5^{60}.3^{20}}\)
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\(\frac{45^{10}.5^{10}}{75^{10}}=\frac{\left(45.5\right)^{10}}{75^{10}}=\frac{225^{10}}{75^{10}}=\left(\frac{225}{75}\right)^{10}=3^{10}\)
\(\frac{\left(0,8\right)^5}{\left(0,4\right)^6}=\frac{\left(0,4.2\right)^5}{\left(0,4\right)^6}=\frac{\left(0,4\right)^5.2^5}{\left(0,4\right)^6}=\frac{2^5}{0,4}=\frac{32}{0,4}=80\)
\(\frac{45^{10}.5^{10}}{75^{10}}=\frac{\left(45.5\right)^{10}}{75^{10}}=\left(\frac{225}{75}\right)^{10}=3^{10}\)
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Ta có : \(\frac{45^{10}.5^{20}}{75^{15}}=\frac{9^{10}.5^{10}.5^{20}}{3^{15}.25^{15}}=\frac{\left(3^2\right)^{10}.5^{30}}{3^{15}.\left(5^2\right)^{15}}=\frac{3^{20}.5^{30}}{3^{15}.5^{30}}=3^5\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{45^{10}.5^{20}}{75^{15}}=\frac{3^{20}.5^{10}.5^{20}}{3^{15}.5^{30}}=\frac{3^{20}.5^{30}}{3^{15}.5^{30}}=3^5=243\)
.Check mk nhá •<3 •
từ đề bài ta có
\(\frac{45^5\cdot5^{10}}{75^5}=\frac{\left(15\cdot3\right)^5\cdot5^{10}}{\left(15\cdot5\right)^5}=\frac{15^5\cdot3^5\cdot5^{10}}{15^5\cdot5^5}=\frac{3^5\cdot5^5}{1}=15^5=759375\)