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\(=\dfrac{\left(3^2\cdot5\right)^{10}\cdot5^{20}}{\left(3\cdot5^2\right)^{15}}=\dfrac{3^{20}\cdot5^{10}\cdot5^{20}}{3^{15}\cdot5^{30}}=3^5=243\)
\(\dfrac{45^{10}.5^{20}}{75^{15}}\)
\(=\dfrac{9^{10}.5^{10}.5^{20}}{25^{15}.3^{15}}\)
\(=\dfrac{3^{20}.5^{30}}{5^{30}.3^{15}}\)
\(=3^5=243\)
4510.105/7515 = (32.5)10 . 520/(3. 52)15 = 320.530/315.530 = 35 = 243
\(=\dfrac{5^{10}\cdot3^{20}\cdot5^{20}}{\left(3\cdot5^2\right)^{15}}=\dfrac{5^{30}\cdot3^{20}}{5^{30}\cdot3^{15}}=3^5=243\)
\(\frac{45^{10}\cdot5^{20}}{75^{15}}=\frac{9^{10}\cdot5^{10}\cdot5^{20}}{3^{15}\cdot25^{15}}=\frac{3^{20}\cdot5^{30}}{3^{15}\cdot5^{30}}=3^5\)
Ta có: 7520 = (52 . 3)20 = 540 . 320
4510 . 2515 = (32 . 5)10 . (52)15 = 320 . 510 . 530 = 320 . 540
=> 7520 = 4510 . 2515 (= 320 . 540)
\(\frac{45^{10}.5^{20}}{75^{15}}\)
\(=\frac{45^{10}.\left(5^2\right)^{10}}{75^{15}}=\frac{45^{10}.25^{10}}{3^{15}.25^{15}}\)
\(=\frac{3^{10}.15^{10}}{3^{15}.25^5}=\frac{3^{10}.5^{10}}{5^5.5^5}\)
\(=3^{10}=59049\)
45^20.5^20/75^15
=(45.5)^20/75^15
=225^20/75^15
=(75.3)^20/75^15
=75^20.3^20/75^15
=75^5.3^20
=75^5.(3^4)^5
=75^5.81^5
=(75.81)^5=6075^5
\(\frac{45^{20}.5^{20}}{75^{15}}=\frac{\left(3.15\right)^{20}.5^{20}}{75^{15}}\)
\(=\frac{3^{20}.15^{20}.5^{20}}{75^{15}}\)
\(=\frac{75^{20}.3^{20}}{75^{15}}\)
\(=\) \(75^5.3^{20}=8,274302827.10^{18}\)