Question

PLEASE HELP 20 POINTS

Answer 1

Answer:

$x^7\sqrt{x}$

Explanation:

$\sqrt{x^{15}}$

apply exponent rule:

$\sqrt{x^{14}x}$    

apply radical rule:

$\sqrt{x^{14}}\sqrt{x}$

simplify more:

$\sqrt{x^{7*2}}\sqrt{x}$

final answer:

$x^7\sqrt{x}$

Answer 2

Answer:

$x^7\sqrt{x}$

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 $\sqrt{ab} =\sqrt{a}\sqrt{b}$:

$\implies \sqrt{x^{14}x}=\sqrt{x^{14}} \sqrt{x}$

Apply the radical rule $\sqrt[a]{x^b} =x^{\frac{b}{a}}$:

$\implies \sqrt{x^{14}} \sqrt{x}=x^{\frac{14}{2}}\sqrt{x}=x^7\sqrt{x}$