ГДЗ по Алгебре 7 Класс Номер 574 Дорофеев, Суворова — Подробные Ответы

а) \(\frac{10^3}{2^2}\)

б) \(8^{12} \cdot 2^{30}\)

в) \(100^4 : 50^4\)

г) \(25^3 \cdot \left(\frac{1}{5}\right)^6\)

д) \(\frac{6^6}{3^5}\)

е) \(9^5 \cdot 3^9\)

ж) \(7^3 : 14^3\)

з) \(16^4 \cdot \left(\frac{1}{4}\right)^8\)

а) \(\frac{10^3}{2^3} = \left(\frac{10}{2}\right)^3 = 5^3 = 125.\)

б) \(8^{12} : 2^{30} = (2^3)^{12} : 2^{30} = 2^{36} : 2^{30} = 2^{36-30} = 2^6 = 64.\)

в) \(100^4 : 50^4 = \left(\frac{100}{50}\right)^4 = 2^4 = 16.\)

г) \(25^3 \cdot \left(\frac{1}{5}\right)^6 = (5^2)^3 \cdot \frac{1}{5^6} = 5^6 \cdot \frac{1}{5^6} = \frac{5^6}{5^6} = 1.\)

д) \(\frac{6^6}{3^6} = \left(\frac{6}{3}\right)^6 = 2^6 = 64.\)

е) \(9^5 : 3^9 = (3^2)^5 : 3^9 = 3^{10} : 3^9 = 3^{10-9} = 3.\)

ж) \(7^3 : 14^3 = \left(\frac{7}{14}\right)^3 = \left(\frac{1}{2}\right)^3 = \frac{1}{8}.\)

з) \(16^4 \cdot \left(\frac{1}{4}\right)^8 = (4^2)^4 \cdot \frac{1}{4^8} = 4^8 \cdot \frac{1}{4^8} = \frac{4^8}{4^8} = 1.\)

а) \(\frac{10^3}{2^3} = \left(\frac{10}{2}\right)^3 = 5^3 = 125.\)

б) \(8^{12} : 2^{30} = (2^3)^{12} : 2^{30} = 2^{36} : 2^{30} = 2^{36-30} = 2^6 = 64.\)

в) \(100^4 : 50^4 = \left(\frac{100}{50}\right)^4 = 2^4 = 16.\)

г) \(25^3 \cdot \left(\frac{1}{5}\right)^6 = (5^2)^3 \cdot \left(\frac{1}{5}\right)^6 = 5^{2 \cdot 3} \cdot \frac{1}{5^6} = 5^6 \cdot \frac{1}{5^6} = \frac{5^6}{5^6} = 1.\)

д) \(\frac{6^6}{3^6} = \left(\frac{6}{3}\right)^6 = 2^6 = 64.\)

е) \(9^5 : 3^9 = (3^2)^5 : 3^9 = 3^{2 \cdot 5} : 3^9 = 3^{10} : 3^9 = 3^{10-9} = 3^1 = 3.\)

ж) \(7^3 : 14^3 = \left(\frac{7}{14}\right)^3 = \left(\frac{1}{2}\right)^3 = \frac{1^3}{2^3} = \frac{1}{8}.\)

з) \(16^4 \cdot \left(\frac{1}{4}\right)^8 = (4^2)^4 \cdot \left(\frac{1}{4}\right)^8 = 4^{2 \cdot 4} \cdot \frac{1}{4^8} = 4^8 \cdot \frac{1}{4^8} = \frac{4^8}{4^8} = 1.\)