Упр.431 ГДЗ Макарычев 7 класс (Алгебра)

а) 5^6 : 5^4;
б) 10^15 : 10^12;
в) 0,5^10 : 0,5^7;
г) (1*1/3)8:(1*1/3)6;
д) 2,7313 : 2,7312;
е) (-2/3)7:(-2/3)4.

1. $$5^6 : 5^4 = 5^{6-4} = 5^2 = 25$$

2. $$10^{15} : 10^{12} = 10^{15-12} = 10^3 = 1000$$

3. $$0{,}5^{10} : 0{,}5^7 = 0{,}5^{10-7} = 0{,}5^3 = 0{,}125$$

4. $$\left(1\frac{1}{3}\right)^8 : \left(1\frac{1}{3}\right)^6 = \left(1\frac{1}{3}\right)^{8-6} = \left(1\frac{1}{3}\right)^2$$

   $$1\frac{1}{3}=\frac{4}{3}, \quad \left(\frac{4}{3}\right)^2=\frac{16}{9}=1\frac{7}{9}$$

5. $$2{,}73^{13} : 2{,}73^{12} = 2{,}73^{13-12} = 2{,}73$$

6. $$\left(-\frac{2}{3}\right)^7 : \left(-\frac{2}{3}\right)^4 = \left(-\frac{2}{3}\right)^{7-4} = \left(-\frac{2}{3}\right)^3 = -\frac{8}{27}$$

Ответ

а) $$25$$; б) $$1000$$; в) $$0{,}125$$; г) $$1\frac{7}{9}$$; д) $$2{,}73$$; е) $$-\frac{8}{27}$$.