Uzasadnij, że :
![\sqrt[6]{9} = \sqrt[3]{3} \\ \sqrt[4] a^{9} = a^{2} x (razy) \sqrt[4]{a} , gdy a \geq 0](https://tex.z-dn.net/?f=+%5Csqrt%5B6%5D%7B9%7D+%3D+%5Csqrt%5B3%5D%7B3%7D+%5C%5C+%5Csqrt%5B4%5D+a%5E%7B9%7D+%3D+a%5E%7B2%7D+x+%28razy%29+%5Csqrt%5B4%5D%7Ba%7D+%2C+gdy+a+%5Cgeq+0 "\sqrt[6]{9} = \sqrt[3]{3} \\ \sqrt[4] a^{9} = a^{2} x (razy) \sqrt[4]{a} , gdy a \geq 0")
wik8947201
![\\\sqrt[6]9=9^{\frac16}=(3^2)^{\frac16}=3^{\frac13}=\sqrt[3]3 \\ \\\sqrt[4]{a^9}=a^{\frac94}=a^{2+\frac14}=a^2*a^{\frac14}=a^2*\sqrt[4]a, \ a\geq0](https://tex.z-dn.net/?f=%5C%5C%5Csqrt%5B6%5D9%3D9%5E%7B%5Cfrac16%7D%3D%283%5E2%29%5E%7B%5Cfrac16%7D%3D3%5E%7B%5Cfrac13%7D%3D%5Csqrt%5B3%5D3%0A%5C%5C%0A%5C%5C%5Csqrt%5B4%5D%7Ba%5E9%7D%3Da%5E%7B%5Cfrac94%7D%3Da%5E%7B2%2B%5Cfrac14%7D%3Da%5E2%2Aa%5E%7B%5Cfrac14%7D%3Da%5E2%2A%5Csqrt%5B4%5Da%2C+%5C+a%5Cgeq0 "\\\sqrt[6]9=9^{\frac16}=(3^2)^{\frac16}=3^{\frac13}=\sqrt[3]3 \\ \\\sqrt[4]{a^9}=a^{\frac94}=a^{2+\frac14}=a^2*a^{\frac14}=a^2*\sqrt[4]a, \ a\geq0")
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TigerXP
![\sqrt[6]{9} = \sqrt[6]{3^2} =3^{ \frac{2}{6} }=3^{ \frac{1}{3} }= \sqrt[3]{3}](https://tex.z-dn.net/?f=+%5Csqrt%5B6%5D%7B9%7D+%3D+%5Csqrt%5B6%5D%7B3%5E2%7D+%3D3%5E%7B+%5Cfrac%7B2%7D%7B6%7D+%7D%3D3%5E%7B+%5Cfrac%7B1%7D%7B3%7D+%7D%3D+%5Csqrt%5B3%5D%7B3%7D+ "\sqrt[6]{9} = \sqrt[6]{3^2} =3^{ \frac{2}{6} }=3^{ \frac{1}{3} }= \sqrt[3]{3}")
![\mathrm{L} = \sqrt[4]{a^9} =a^{ \frac{9}{4} } \\\\ \mathrm{P}=a^2 \cdot \sqrt[4]{a} =a^2 \cdot a^{ \frac{1}{4} }=a^{2+ \frac{1}{4} }= a^{ \frac{9}{4} } = \mathrm{L}, \quad \mathrm{dla} \quad a \geq 0](https://tex.z-dn.net/?f=+%5Cmathrm%7BL%7D+%3D++%5Csqrt%5B4%5D%7Ba%5E9%7D+%3Da%5E%7B+%5Cfrac%7B9%7D%7B4%7D+%7D+%5C%5C%5C%5C%0A%5Cmathrm%7BP%7D%3Da%5E2+%5Ccdot+++%5Csqrt%5B4%5D%7Ba%7D++%3Da%5E2+%5Ccdot+a%5E%7B+%5Cfrac%7B1%7D%7B4%7D+%7D%3Da%5E%7B2%2B+%5Cfrac%7B1%7D%7B4%7D+%7D%3D+a%5E%7B+%5Cfrac%7B9%7D%7B4%7D+%7D+%3D++%5Cmathrm%7BL%7D%2C+%5Cquad+%5Cmathrm%7Bdla%7D+%5Cquad+a+%5Cgeq+0+ "\mathrm{L} = \sqrt[4]{a^9} =a^{ \frac{9}{4} } \\\\ \mathrm{P}=a^2 \cdot \sqrt[4]{a} =a^2 \cdot a^{ \frac{1}{4} }=a^{2+ \frac{1}{4} }= a^{ \frac{9}{4} } = \mathrm{L}, \quad \mathrm{dla} \quad a \geq 0")
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