what is the simplified form of $sqrt{64x^{16}}$?\n$8x^{4}$\n$8x^{8}$\n$32x^{4}$\n$32x^{8}$

Explanation:

Step1: Separate the square - root

Use the property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ where $a = 64$ and $b=x^{16}$. So, $\sqrt{64x^{16}}=\sqrt{64}\cdot\sqrt{x^{16}}$.

Step2: Calculate $\sqrt{64}$

We know that $8\times8 = 64$, so $\sqrt{64}=8$.

Step3: Calculate $\sqrt{x^{16}}$

Use the property $\sqrt{x^{n}}=x^{\frac{n}{2}}$. For $n = 16$, $\sqrt{x^{16}}=x^{\frac{16}{2}}=x^{8}$.

Step4: Combine the results

$\sqrt{64}\cdot\sqrt{x^{16}}=8x^{8}$.

Answer:

B. $8x^{8}$