Question

Please help me with Algebra 2 problems.

Answer 1

Answer:

$5)\ \ \left( x^{8}y^{4}\right)^{\frac{1}{10} } +3\left( x^{\frac{1}{5}}y^{\frac{1}{10} \right)^4=4x^{\frac{4}{5}}y^{\frac{2}{5}}$

$6)\ \ \frac{2\sqrt{9^{5}} +7\sqrt{9^{5}} }{\sqrt{9^{7}} }=1$

Step-by-step explanation:

$\left( x^{8}y^{4}\right)^{\frac{1}{10} } +3\left( x^{\frac{1}{5}}y^{\frac{1}{10} \right)^4$

$=x^{\frac{8}{10}}y^{\frac{4}{10}} +3x^{\frac{4}{5}}y^{\frac{4}{10} }$

$=x^{\frac{4}{5}}y^{\frac{2}{5}} +3x^{\frac{4}{5}}y^{\frac{2}{5} }$

$=x^{\frac{4}{5}}y^{\frac{2}{5}}\times(1+3)$

$=4x^{\frac{4}{5}}y^{\frac{2}{5}}$

……………………………………

$\frac{2\sqrt{9^{5}} +7\sqrt{9^{5}} }{\sqrt{9^{7}} }$

$=\frac{(2+7) \times\sqrt{9^{5}} }{\sqrt{9^{2}} \times \sqrt{9^{5}} }$

$=\frac{9 \times\sqrt{9^{5}} }{9 \times \sqrt{9^{5}} }$

$=1$