0\; ,\; \; a\sqrt[4]2=\sqrt[4]{2a^4}\\\\x<0\; ,\; \; x\sqrt[4]5=-\sqrt[4]{5x^4}\\\\5)\; \; \frac{\sqrt[12]{a}\cdot \sqrt[24]{a}}{a\sqrt[8]{a}}=\frac{\sqrt[24]{a^2}\cdot \sqrt[24]{a}}{\sqrt[8]{a^9}}=\frac{\sqrt[24]{a^3}}{\sqrt[24]{a^{27}}}=\sqrt[24]{\frac{a^3}{a^{27}}}=\sqrt[24]{\frac{1}{a^{24}}}=\frac{1}{a}" alt="4a)\; \; 3\sqrt[3]3=\sqrt[3]{3^3\cdot 3}=\sqrt[3]{81}\\\\a>0\; ,\; \; a\sqrt[4]2=\sqrt[4]{2a^4}\\\\x<0\; ,\; \; x\sqrt[4]5=-\sqrt[4]{5x^4}\\\\5)\; \; \frac{\sqrt[12]{a}\cdot \sqrt[24]{a}}{a\sqrt[8]{a}}=\frac{\sqrt[24]{a^2}\cdot \sqrt[24]{a}}{\sqrt[8]{a^9}}=\frac{\sqrt[24]{a^3}}{\sqrt[24]{a^{27}}}=\sqrt[24]{\frac{a^3}{a^{27}}}=\sqrt[24]{\frac{1}{a^{24}}}=\frac{1}{a}" align="absmiddle" class="latex-formula">
![4b)\; \; \sqrt[5]{\frac{243z^6}{\sqrt[3]{z^9}}}=\sqrt[5]{\frac{3^5z^6}{z^3}}=3\sqrt[5]{z^3}\\\\4c)\; \; \sqrt[4]{243a^5b^5}\cdot \sqrt[4]{\frac{1}{3}a^3b^3}=\sqrt[4]{3^5a^5b^5\cdot 3^{-1}a^3b^3}=\sqrt[4]{3^4a^8b^8}=3a^2b^2\\\\5a)\; \; y=\sqrt{x^2-81}\; ,\\\\ODZ:\; \; x^2-81\geq 0\\\\(x-9)(x+9)\geq 0\quad +++[-9\, ]---[\, 9\, ]+++\\\\x\in [-9,9\, ]\\\\5b)\; \; y=\sqrt[5]{x^2-7x}\; ,\; \quad ODZ:\; \; x\in (-\infty ,+\infty )](https://tex.z-dn.net/?f=4b%29%5C%3B%20%5C%3B%20%5Csqrt%5B5%5D%7B%5Cfrac%7B243z%5E6%7D%7B%5Csqrt%5B3%5D%7Bz%5E9%7D%7D%7D%3D%5Csqrt%5B5%5D%7B%5Cfrac%7B3%5E5z%5E6%7D%7Bz%5E3%7D%7D%3D3%5Csqrt%5B5%5D%7Bz%5E3%7D%5C%5C%5C%5C4c%29%5C%3B%20%5C%3B%20%5Csqrt%5B4%5D%7B243a%5E5b%5E5%7D%5Ccdot%20%5Csqrt%5B4%5D%7B%5Cfrac%7B1%7D%7B3%7Da%5E3b%5E3%7D%3D%5Csqrt%5B4%5D%7B3%5E5a%5E5b%5E5%5Ccdot%203%5E%7B-1%7Da%5E3b%5E3%7D%3D%5Csqrt%5B4%5D%7B3%5E4a%5E8b%5E8%7D%3D3a%5E2b%5E2%5C%5C%5C%5C5a%29%5C%3B%20%5C%3B%20y%3D%5Csqrt%7Bx%5E2-81%7D%5C%3B%20%2C%5C%5C%5C%5CODZ%3A%5C%3B%20%5C%3B%20x%5E2-81%5Cgeq%200%5C%5C%5C%5C%28x-9%29%28x%2B9%29%5Cgeq%200%5Cquad%20%2B%2B%2B%5B-9%5C%2C%20%5D---%5B%5C%2C%209%5C%2C%20%5D%2B%2B%2B%5C%5C%5C%5Cx%5Cin%20%5B-9%2C9%5C%2C%20%5D%5C%5C%5C%5C5b%29%5C%3B%20%5C%3B%20y%3D%5Csqrt%5B5%5D%7Bx%5E2-7x%7D%5C%3B%20%2C%5C%3B%20%5Cquad%20%20ODZ%3A%5C%3B%20%5C%3B%20x%5Cin%20%28-%5Cinfty%20%2C%2B%5Cinfty%20%29 "4b)\; \; \sqrt[5]{\frac{243z^6}{\sqrt[3]{z^9}}}=\sqrt[5]{\frac{3^5z^6}{z^3}}=3\sqrt[5]{z^3}\\\\4c)\; \; \sqrt[4]{243a^5b^5}\cdot \sqrt[4]{\frac{1}{3}a^3b^3}=\sqrt[4]{3^5a^5b^5\cdot 3^{-1}a^3b^3}=\sqrt[4]{3^4a^8b^8}=3a^2b^2\\\\5a)\; \; y=\sqrt{x^2-81}\; ,\\\\ODZ:\; \; x^2-81\geq 0\\\\(x-9)(x+9)\geq 0\quad +++[-9\, ]---[\, 9\, ]+++\\\\x\in [-9,9\, ]\\\\5b)\; \; y=\sqrt[5]{x^2-7x}\; ,\; \quad ODZ:\; \; x\in (-\infty ,+\infty )")