Answer:
[tex]5)\ \ \left( x^{8}y^{4}\right)^{\frac{1}{10} } +3\left( x^{\frac{1}{5}}y^{\frac{1}{10} \right)^4=4x^{\frac{4}{5}}y^{\frac{2}{5}}[/tex]
[tex]6)\ \ \frac{2\sqrt{9^{5}} +7\sqrt{9^{5}} }{\sqrt{9^{7}} }=1[/tex]
Step-by-step explanation:
[tex]\left( x^{8}y^{4}\right)^{\frac{1}{10} } +3\left( x^{\frac{1}{5}}y^{\frac{1}{10} \right)^4[/tex]
[tex]=x^{\frac{8}{10}}y^{\frac{4}{10}} +3x^{\frac{4}{5}}y^{\frac{4}{10} }[/tex]
[tex]=x^{\frac{4}{5}}y^{\frac{2}{5}} +3x^{\frac{4}{5}}y^{\frac{2}{5} }[/tex]
[tex]=x^{\frac{4}{5}}y^{\frac{2}{5}}\times(1+3)[/tex]
[tex]=4x^{\frac{4}{5}}y^{\frac{2}{5}}[/tex]
……………………………………
[tex]\frac{2\sqrt{9^{5}} +7\sqrt{9^{5}} }{\sqrt{9^{7}} }[/tex]
[tex]=\frac{(2+7) \times\sqrt{9^{5}} }{\sqrt{9^{2}} \times \sqrt{9^{5}} }[/tex]
[tex]=\frac{9 \times\sqrt{9^{5}} }{9 \times \sqrt{9^{5}} }[/tex]
[tex]=1[/tex]
