Упр.45 ГДЗ Колягин Ткачёва 9 класс (Алгебра)

1) (a^6 b^7)^(1/5):(ab^2)^(1/5); 2) (81x^4y)^(1/3):(3xy)^(1/3);
3) (3x/y^2)^(1/3):(y/9x^2)^(1/3); 4) (2b/a^3)^(1/4):(a/8b^3)^(1/4).

1. $$\left(a^6b^7\right)^{\frac15}:\left(ab^2\right)^{\frac15} =\left(\frac{a^6b^7}{ab^2}\right)^{\frac15} =\left(a^5b^5\right)^{\frac15} =ab.$$

2. $$\left(81x^4y\right)^{\frac13}:\left(3xy\right)^{\frac13} =\left(\frac{81x^4y}{3xy}\right)^{\frac13} =\left(27x^3\right)^{\frac13} =3x.$$

3. $$\left(\frac{3x}{y^2}\right)^{\frac13}:\left(\frac{y}{9x^2}\right)^{\frac13} =\left(\frac{3x}{y^2}\cdot\frac{9x^2}{y}\right)^{\frac13} =\left(\frac{27x^3}{y^3}\right)^{\frac13} =\frac{3x}{y}.$$

4. $$\left(\frac{2b}{a^3}\right)^{\frac14}:\left(\frac{a}{8b^3}\right)^{\frac14} =\left(\frac{2b}{a^3}\cdot\frac{8b^3}{a}\right)^{\frac14} =\left(\frac{16b^4}{a^4}\right)^{\frac14} =\frac{2b}{a}.$$

Ответ

1) $$ab$$; 2) $$3x$$; 3) $$\frac{3x}{y}$$; 4) $$\frac{2b}{a}$$.