Question

Помогите пожалуйста!!!!!!​

Answer 1

$1)\ \ \ n\leq 0\ ,\ p\ge 0\\\\\sqrt[4]{81m^8n^{20}p^4}=\sqrt[4]{3^4\cdot (m^2)^4\cdot (n^5)^4\cdot p^4}=3\cdot |\underbrace {m^2}_{\geq 0}|\cdot |\underbrace {n^5}_{\leq 0}|\cdot |\underbrace {p}_{\geq 0}|=\\\\=3\cdot m^2\cdot (-n^5)\cdot p=-3\, m^2\, n^5\, p$

$2)\ \ \ x\leq 0\\\\1,4x\sqrt[8]{256x^{24}}=1,4x\cdot \sqrt[8]{2^8\cdot (x^3)^8}=1,4x\cdot 2\cdot |\underbrace {x^3}_{\leq 0}|=2,8x\cdot (-x^3)=\\\\=-2,8\, x^4\\\\\\3)\ \ \ a<0\ ,\ c<0\\\\\dfrac{\sqrt[12]{a^{12}\, b^{24}\, c^{36}}}{abc}=\dfrac{\sqrt[12]{a^{12}\cdot (b^2)^{12}\cdot (c^3)^{12}}}{abc}=\dfrac{|a|\cdot |b^2|\cdot |c^3|}{abc}=\\\\\\=\dfrac{(-a)\cdot b^2\cdot (-c^3)}{abc}=\dfrac{b\cdot c^2}{1}=b\, c^2$

$\star \ \ \ |a|=\left\{\begin{array}{l}+a\, ,\, esli\ a\geq 0\ ,\\-a\, ,\, esli\ a<0\ .\end{array}\right$