$$  $$$$  $$$$ \sqrt{16x^8}\text{ Simplify the following using radical properties. } $$

We are given the expression $ \sqrt{16x^8} $ and asked to simplify it using radical properties.

### Step 1: Break the square root into two parts.
We can use the property of square roots that states:
\[
\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}
\]
So, we can rewrite the given expression as:
\[
\sqrt{16x^8} = \sqrt{16} \cdot \sqrt{x^8}
\]

### Step 2: Simplify each part.
- $ \sqrt{16} = 4 $, because $ 4^2 = 16 $.
- For $ \sqrt{x^8} $, we apply the rule $ \sqrt{x^n} = x^{n/2} $. Thus:
  \[
  \sqrt{x^8} = x^{8/2} = x^4
  \]

### Step 3: Combine the results.
Now, putting the two parts together:
\[
\sqrt{16x^8} = 4 \cdot x^4
\]

Thus, the simplified form of $ \sqrt{16x^8} $ is:
\[
4x^4
\]

Would you like more details on radical properties or have any other questions?

### 5 Related Questions:
1. How do you simplify higher-order radicals like $ \sqrt[3]{27x^6} $?
2. What are the key properties of radicals and exponents?
3. How can you simplify $ \sqrt{25x^{10}} $?
4. How do fractional exponents relate to radicals?
5. What is the general formula for simplifying $ \sqrt{a^m b^n} $?

### Tip:
Always check if both numerical and variable terms under the radical can be simplified separately. This helps in applying radical properties more easily.

$ \sqrt{16x^8} $ Simplify the following using radical properties.

Learn how to simplify the expression $ \sqrt{16x^8} $ step-by-step using radical properties. This solution breaks down the use of square roots and exponent rules, perfect for students in Grades 9-10.

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