CMR 75^20=4^10.5^30
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(75^{20}=\left(3.5^2\right)^{20}=3^{20}.5^{40}=9^{10}.5^{10}.5^{30}=\left(9.5\right)^{10}.5^{30}=45^{10}.5^{30}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a, Thiếu 1 vế
b, Xét vế trái:
7520 = 2520 . 320
= 520. 520 . 320
= 530.510.310.310
= 530.4510 = Vế phải
=> 7520 = 4510.530 (Đpcm)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) ...
b) 75^20 = 3^20 . 25^20 = 5^40 . 9^10 = 5^30.45^10
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\dfrac{45^{10}.5^{20}}{75^{15}}\)
\(=\dfrac{9^{10}.5^{10}.5^{20}}{25^{15}.3^{15}}\)
\(=\dfrac{3^{20}.5^{30}}{5^{30}.3^{15}}\)
\(=3^5=243\)
![](https://rs.olm.vn/images/avt/0.png?1311)
4510.105/7515 = (32.5)10 . 520/(3. 52)15 = 320.530/315.530 = 35 = 243
![](https://rs.olm.vn/images/avt/0.png?1311)
a, bạn coi đề coi có đúng ko
b,VT= 4510.530
=310.310.510.530
=320.540
=320.520.520
=1520.520
=7520=>VP
![](https://rs.olm.vn/images/avt/0.png?1311)
\(=\dfrac{5^{10}\cdot3^{20}\cdot5^{20}}{\left(3\cdot5^2\right)^{15}}=\dfrac{5^{30}\cdot3^{20}}{5^{30}\cdot3^{15}}=3^5=243\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{45^{10}.5^{20}}{75^{15}}\)
\(=\frac{45^{10}.\left(5^2\right)^{10}}{75^{15}}=\frac{45^{10}.25^{10}}{3^{15}.25^{15}}\)
\(=\frac{3^{10}.15^{10}}{3^{15}.25^5}=\frac{3^{10}.5^{10}}{5^5.5^5}\)
\(=3^{10}=59049\)