https://file.aiquickdraw.com/mathbot/file/1730725459480o4h1gcs0.jpg

The expression in the image is:

\[
\frac{\sqrt[4]{625}}{\sqrt{625}}
\]

Let's solve it step by step.

### Step 1: Simplify \(\sqrt[4]{625}\)

1. We know that \(625 = 5^4\).
2. Thus, \(\sqrt[4]{625} = \sqrt[4]{5^4} = 5\).

### Step 2: Simplify \(\sqrt{625}\)

1. \(\sqrt{625} = \sqrt{5^4} = 25\).

### Step 3: Put it all together

The expression now becomes:
\[
\frac{\sqrt[4]{625}}{\sqrt{625}} = \frac{5}{25}
\]

### Step 4: Simplify the fraction

\[
\frac{5}{25} = \frac{1}{5}
\]

### Final Answer

\[
\frac{\sqrt[4]{625}}{\sqrt{625}} = \frac{1}{5}
\]

Would you like further details or have any questions?

---

Here are five related questions to consider:

1. How do you determine the fourth root of a number?
2. What are the properties of exponents when dealing with roots?
3. How can you simplify expressions with higher-order roots in the numerator and denominator?
4. What other numbers have integer values for both square roots and fourth roots?
5. Why does \(\sqrt[4]{625} = 5\) simplify to an integer?

**Tip:** To simplify roots and powers, expressing the number as a base with an exponent can help quickly find values for roots.

Simplify the expression \( \frac{\sqrt[4]{625}}{\sqrt{625}} \).

Learn how to simplify the expression \( \frac{\sqrt[4]{625}}{\sqrt{625}} \) with a detailed, step-by-step solution. This problem involves simplifying roots and understanding exponent rules, suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation