Question

Does anyone know the answer to this algebra 2 question?

Answer 1

ans is second one 4√20/2

Answer 2

`\frac{(10)^{(1)/(2)}}{8^{(1)/(4)}}`

Multiplying numerator and Denominator by
`(2)^{(1)/(4)}}`

`=\frac{(10)^{(1)/(2)}}{8^{(1)/(4)}}* \frac{2^{(1)/(4)}}{2^{(1)/(4)}}\\\\=\frac{(10^2)^{(1)/(4)}}{2^{(3)/(4)}* 2^{(1)/(4)}}* 2^{(1)/(4)}}\\\\=\frac{(100 * 2)^{(1)/(4)}}{2^{(3)/(4)+(1)/(4)}}\\\\=\frac{(200)^{(1)/(4)}}{2^(4)/(4)}\\\\=\frac{(200)^{(1)/(4)}}{2}`

Used the following law of indices

`1.(x^a)/(x^b)=x^(a-b)\\\\2. x^a * x^b=x^(a+b)`

`3.x^m * a^m=(ax)^m`

Option A:
`\frac{(200)^{(1)/(4)}}{2}` equivalent to
`\frac{(10)^{(1)/(2)}}{8^{(1)/(4)}}`