https://file.aiquickdraw.com/mathbot/file/172904859532765a0lalw.jpg

The expression in the image is:

\[
\frac{\sqrt[4]{128}}{\sqrt[4]{8}}
\]

To simplify this:

### Step 1: Break down the radicals
We can rewrite the expression inside the fourth roots as powers of 2 since both 128 and 8 are powers of 2.

- \(128 = 2^7\)
- \(8 = 2^3\)

The expression now becomes:

\[
\frac{\sqrt[4]{2^7}}{\sqrt[4]{2^3}}
\]

### Step 2: Apply the fourth root
The fourth root of a power simplifies as follows:

\[
\sqrt[4]{2^a} = 2^{a/4}
\]

So, the expression becomes:

\[
\frac{2^{7/4}}{2^{3/4}}
\]

### Step 3: Use the properties of exponents
When dividing powers with the same base, you subtract the exponents:

\[
2^{(7/4) - (3/4)} = 2^{4/4} = 2^1
\]

Thus, the expression simplifies to:

\[
2
\]

### Final Answer:
\[
\frac{\sqrt[4]{128}}{\sqrt[4]{8}} = 2
\]

Would you like any further details or clarifications?

### Related questions:
1. How do you simplify other radical expressions involving different roots?
2. How do powers of numbers behave under roots of higher degrees?
3. How can we simplify the ratio of two radicals with different bases?
4. How would this problem change if the roots were cubic instead of fourth roots?
5. What are the general properties of exponents when dealing with radicals?

### Tip:
When simplifying roots of powers, expressing the numbers as powers of a common base often makes the process easier!

Simplify the expression \(\frac{\sqrt[4]{128}}{\sqrt[4]{8}}\).

Learn how to simplify the expression involving fourth roots \(\frac{\sqrt[4]{128}}{\sqrt[4]{8}}\) using exponent rules and radicals. This problem focuses on properties of exponents and simplifying radical expressions. Suitable for students in Grades 8-10.

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