Question

Please help me with Algebra 2 problems.

Answer 1

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

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

Explanation:

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

`=x^{(8)/(10)}y^{(4)/(10)} +3x^{(4)/(5)}y^{(4)/(10) }`

`=x^{(4)/(5)}y^{(2)/(5)} +3x^{(4)/(5)}y^{(2)/(5) }`

`=x^{(4)/(5)}y^{(2)/(5)}*(1+3)`

`=4x^{(4)/(5)}y^{(2)/(5)}`

……………………………………

`\frac{2\sqrt{9^(5)} +7\sqrt{9^(5)} }{\sqrt{9^(7)} }`

`=\frac{(2+7) *\sqrt{9^(5)} }{\sqrt{9^(2)} * \sqrt{9^(5)} }`

`=\frac{9 *\sqrt{9^(5)} }{9 * \sqrt{9^(5)} }`

`=1`