Question

СРОЧНО!
с подробным решением

Answer 1

извини за чирканье и заплатку

Answer 2

$4)\; \; \sqrt[3]{\sqrt{a}}+\sqrt[18]{a^3}=\sqrt[6]{a}+\sqrt[6]{a}=2\sqrt[n6]{a}\\\\6a\sqrt[4]{a^5}:3\sqrt[4]{a}= \frac{6a\cdot a^{5/4}}{3a^{1/4}}=\frac{2a^{9/4}}{a^{1/4}}=2a^2\\\\\frac{a^{1/4}-4}{a^{1/4}+4a^{1/8}+4}=\frac{(a^{1/8}-2)(a^{1/8}+2)}{(a^{1/8}+2)^2}=\frac{a^{1/8-2}}{a^{1/8}+2}$

$5)\; \; \Big (\frac{a^{0,5}-b^{0,5}}{a^{0,5}+b^{0,5}}+\frac{2a^{0,5}\cdot b^{0,5}}{a-b}\Big )\cdot \frac{a-2a^{0,5}b^{0,5}+b}{a+b}=\\\\=\Big (\frac{a^{0,5}-b^{0,5}}{a^{0,5}+b^{0,5}}+\frac{2a^{0,5}b^{0,5}}{(a^{0,5}-b^{0,5})(a^{0,5}+b^{0,5})}\Big )\cdot \frac{(a^{0,5}-b^{0,5})^2}{a+b}=\\\\=\frac{(a^{0,5}-b^{0,5})^2+2a^{0,5}b^{0,5}}{(a^{0,5}-b^{0,5})(a^{0,5}+b^{0,5})}\cdot \frac{(a^{0,5}-b^{0,5})^2}{a+b}=\\\\=\frac{(a+b)(a^{0,5}-b^{0,5})}{(a^{0,5}+b^{0,5})(a+b)}=\frac{a^{0,5}-b^{0,5}}{a^{0,5}+b^{0,5}}=\frac{\sqrt{a}-\sqrt{b}}{\sqrt{a}+\sqrt{b}}=\frac{(\sqrt{a}-\sqrt{b})^2}{a-b}$