Question

Упростите выражение:

Answer 1

$\sqrt[3]{16a^4 b^{12} } : \sqrt[3]{2ab^9}= \sqrt[3]{ \frac{16a^4 b^{12} }{2ab^9} } = \sqrt[3]{8a^3b^3}=2ab$

Answer 2

Решение:
³√(16a^4b^12 : ³√2ab^9=(16a^4b^12)^1/3 : (2ab^9)^1/3=(2^4a^4b^12)^1/3 : (2ab^9)^1/3=
={(2^4/3)*(a^4/3)*(b^12/3)} : {(2^1/3)*(a^1/3)*(b^9/3)}=2^(4/3-1/3)*a^(4/3-1/3)*b^(12/3-9/3)=
=2ab

Ответ: 2ab