452. Найдите значение выражения: a) 2⁴ ⋅ 5⁴; в) 0,25¹⁵ ⋅ 4¹⁵; д) ($$\frac{5}{7}$$)^{10} ⋅ 1,4⁹; б) 4³ ⋅ 25³; г) ($$\frac{2}{3}$$)^7 ⋅ 1,5⁷; e) 0,2⁶ ⋅ 50⁷.

a) $$2^4 \cdot 5^4 = (2 \cdot 5)^4 = 10^4 = 10000$$.

б) $$4^3 \cdot 25^3 = (4 \cdot 25)^3 = 100^3 = 1000000$$.

в) $$0,25^{15} \cdot 4^{15} = (0,25 \cdot 4)^{15} = 1^{15} = 1$$.

г) $$\left(\frac{2}{3}\right)^7 \cdot 1,5^7 = \left(\frac{2}{3} \cdot \frac{3}{2}\right)^7 = 1^7 = 1$$.

д) $$\left(\frac{5}{7}\right)^{10} \cdot 1,4^9 = \left(\frac{5}{7}\right)^{10} \cdot \left(\frac{7}{5}\right)^9 = \frac{5^{10}}{7^{10}} \cdot \frac{7^9}{5^9} = \frac{5^{10} \cdot 7^9}{7^{10} \cdot 5^9} = \frac{5}{7}$$.

e) $$0,2^6 \cdot 50^7 = \left(\frac{1}{5}\right)^6 \cdot 50^7 = \frac{50^7}{5^6} = \frac{(5 \cdot 10)^7}{5^6} = \frac{5^7 \cdot 10^7}{5^6} = 5 \cdot 10^7 = 50000000$$.

Ответ: a) $$10000$$, б) $$1000000$$, в) $$1$$, г) $$1$$, д) $$\frac{5}{7}$$, e) $$50000000$$