№ 18.38 Алгебра = № 34.38 Математика
Обчисліть:
1. $\frac{{216}^3}{{36}^4};$
2. $\frac{{81}^6}{{27}^8};$
3. $\frac{4^8\cdot16}{{64}^3};$
4. $\frac{2^8\cdot{13}^8}{{26}^7}.$
Розв'язок:
1. $\frac{{216}^3}{{36}^4}=\frac{(36\cdot6)^3}{364}=$
$= \frac{{36}^3\cdot6^3}{{36}^4}=\frac{6^3}{36}=\frac{6^3}{6^2}=6;$
2. $\frac{{81}^6}{{27}^8}=\frac{\left(3^4\right)^6}{\left(3^3\right)^8}=\frac{3^{24}}{3^{24}}=1;$
3. $\frac{4^8\cdot16}{{64}^3}=\frac{\left(2^2\right)^8\cdot2^4}{\left(2^6\right)^3}=$
$= \frac{2^{16}\cdot2^4}{2^{18}}=\frac{2^{20}}{2^{18}}=2^2=4;$
4. $\frac{2^8\cdot{13}^8}{{26}^7}=\frac{(2\cdot13)^8}{{26}^7}=$
$= \frac{{26}^8}{{26}^7}={26}^1=26.$