Упр.40 ГДЗ Колягин Ткачёва 9 класс (Алгебра)

1) (30^10·2^15)^(1/5); 2) (2^3·5^6)^(1/3);
3) (3^12·(1/3)^8)^(1/4); 4) (4^12·(1/2)^8)^(1/4).

1. $$\left(30^{10}\cdot 2^{15}\right)^{\frac15}=\left((3\cdot 2)^ {10}\cdot 2^{15}\right)^{\frac15}=\left(3^{10}\cdot 2^{25}\right)^{\frac15}=3^2\cdot 2^5=9\cdot 32=288.$$
2. $$\left(2^3\cdot 5^6\right)^{\frac13}=2^{3\cdot \frac13}\cdot 5^{6\cdot \frac13}=2\cdot 5^2=2\cdot 25=50.$$
3. $$\left(3^{12}\cdot \left(\frac13\right)^8\right)^{\frac14}=\left(3^{12}\cdot 3^{-8}\right)^{\frac14}=\left(3^4\right)^{\frac14}=3.$$
4. $$\left(4^{12}\cdot \left(\frac12\right)^8\right)^{\frac14}=\left((2^2)^{12}\cdot 2^{-8}\right)^{\frac14}=\left(2^{24}\cdot 2^{-8}\right)^{\frac14}=\left(2^{16}\right)^{\frac14}=2^4=16.$$

Ответ

1) $$288$$; 2) $$50$$; 3) $$3$$; 4) $$16$$.