Question

Решите задание по алгебре

Answer 1

$9.25)\ \ n\leq 0\ \ ,\ \ \sqrt[4]{n^4}=|n|=-n\\\\k\leq 0\ \ ,\ \ \sqrt[8]{256k^8}=\sqrt[8]{(2k)^8}=|2k|=-2k\\\\\sqrt[6]{c^{24}}=\sqrt[6]{(c^4)^6}=|c^4|=c^4\\\\b\leq 0\ \ ,\ \ \sqrt{0,25b^{14}}=\sqrt{(0,5b^7)^2}=|0,5b^7|=-0,5b^7\\\\y\geq 0\ \ ,\ \ \sqrt[4]{81x^8y^4}=\sqrt[4]{(3x^2y)^4}=|3x^2y|=3x^2y\\\\a\leq 0\ ,\ b\geq 0\ ,\ \ \sqrt{0,01a^6b^{10}}=\sqrt{(0,1a^3b^5)^2}=|0,1a^3b^5|=-0,1a^3b^5\\\\x\leq 0\ ,\ -1,2x\, \sqrt[6]{64x^{30}}=-1,2x\, \sqrt[6]{(2x^5)^6}=-1,2x\cdot |2x^5|=-1,2x\cdot (-2x^5)=\\\\=2,4x^6$

$9.26)\ \ \sqrt[4]{625a^{24}}=5a^6\\\\b\geq 0\ ,\ \ \sqrt[4]{0,0001b^{20}}=0,1\cdot |b^5|=0,1\, b^5\\\\x\leq 0\ ,\ \ -5\sqrt{4x^2}=-5\cdot 2|x|=-5\cdot 2(-x)=10x\\\\p\geq 0\ ,\ \ \sqrt[10]{p^{30}q^{40}}=p^3q^4\\\\m\leq 0\ ,\ n\leq 0\ ,\ \ \sqrt[12]{m^{36}n^{60}}=|m^3|\cdot |n^5|=(-m^3)\cdot (-n^5)=m^3n^5\\\\b\geq 0\ ,\ c\leq 0\ ,\ \ ab^2\sqrt[4]{a^{48}b^{36}c^{44}}=ab^2\, |a^{12}|\cdot |b^9|\cdot |c^{11}|=ab^2\cdot a^{12}\cdot b^9\cdot (-c^{11})=\\\\=-a^{13}\, b^{11}\, c^{11}$