Question

PLEASE HELP 20 POINTS

Answer 1

`x^7√(x)`

Step-by-step explanation:

`\sqrt{x^(15)} =\sqrt{x^((14+1))}`

Apply the exponent rule
`a^(b+c)=a^b \cdot a^c`

`\implies \sqrt{x^((14+1))}=\sqrt{x^(14)x^1}=\sqrt{x^(14)x}`

Apply the radical rule
`√(ab) =√(a)√(b)`:

`\implies \sqrt{x^(14)x}=\sqrt{x^(14)} √(x)`

Apply the radical rule
`\sqrt[a]{x^b} =x^{(b)/(a)}`:

`\implies \sqrt{x^(14)} √(x)=x^{(14)/(2)}√(x)=x^7√(x)`

Answer 2

`x^7√(x)`

Step-by-step explanation:

`\sqrt{x^(15)}`

apply exponent rule:

`\sqrt{x^(14)x}`

apply radical rule:

`\sqrt{x^(14)}√(x)`

simplify more:

`\sqrt{x^(7*2)}√(x)`

final answer:

`x^7√(x)`