Упр.21.19 ГДЗ Мордкович 7 класс (Алгебра)

а) $$\left(-\frac{5}{7}\right)^3 \cdot \left(-\frac{7}{3}\right)^2$$; б) $$\left(-\frac{7}{8}\right)^{10} \cdot \left(-\frac{8}{7}\right)^{10}$$; в) $$\left(\frac{5}{6}\right)^6 \cdot \left(\frac{12}{5}\right)^6$$; г) $$\left(\frac{3}{4}\right)^4 \cdot \left(\frac{8}{3}\right)^4$$.

1. $$\left(-\frac{5}{7}\right)^3 \cdot \left(-\frac{7}{3}\right)^3 = \left(-\frac{5}{7}\cdot -\frac{7}{3}\right)^3 = \left(\frac{5}{3}\right)^3 = \frac{125}{27} = 4\frac{17}{27}.$$

2. $$\left(-\frac{7}{8}\right)^{10} \cdot \left(-\frac{8}{7}\right)^{10} = \left(-\frac{7}{8}\cdot -\frac{8}{7}\right)^{10} = 1^{10} = 1.$$

3. $$\left(\frac{5}{6}\right)^6 \cdot \left(\frac{12}{5}\right)^6 = \left(\frac{5}{6}\cdot \frac{12}{5}\right)^6 = 2^6 = 64.$$

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

Ответ

а) $$4\frac{17}{27}$$; б) $$1$$; в) $$64$$; г) $$16$$.