Question

Алгебра 8 повторение пройденного

Answer 1

1)-а(-а)^1/2

2)-ав^3(-а)^1/2

Answer 2

Ответ:

$1)\ \ \sqrt{-a^5}=\Big[\ -a^5\geq 0\ \to \ a\leq 0\ \Big]=\sqrt{-a^4\cdot a}=\sqrt{(a^2)^2\cdot (-a)}=\\\\=|\underbrace {a^2}_{\geq 0}|\cdot \sqrt{-a}=a^2\cdot \sqrt{-a}\\\\\\2)\ \ \sqrt{-a^3\, b^6}=\Big[\ -a^3b^6\geq 0\ ,\ b>0\ \ \to \ \ b^6\geq 0\ ,\ -a^3\geq 0\ \to \ a\leq 0\ \Big]=\\\\=\sqrt{(b^3)^2\cdot a^2\cdot (-a)}=|\underbrace {b^3}_{\geq 0}|\cdot |\underbrace {a}_{\leq 0}|\cdot \sqrt{-a}=b^3\cdot (-a)\cdot \sqrt{-a}=-a\, b^3\cdot \sqrt{-a}$