https://file.aiquickdraw.com/mathbot/file/1725259297759jlvdmc09.jpg

The expression shown in the image is:

\[
\frac{r^{7/5}}{r} \div \frac{dr}{r^3}
\]

To perform the indicated operation, we need to simplify the expression step by step.

### Step 1: Simplify each fraction

1. **Simplify the first fraction** \(\frac{r^{7/5}}{r}\):

   \[
   \frac{r^{7/5}}{r} = r^{7/5 - 1} = r^{7/5 - 5/5} = r^{2/5}
   \]

2. **Simplify the second fraction** \(\frac{dr}{r^3}\):

   This fraction remains as \(\frac{dr}{r^3}\) because it's already simplified.

### Step 2: Divide the two fractions

Dividing by a fraction is the same as multiplying by its reciprocal:

\[
\frac{r^{2/5}}{1} \div \frac{dr}{r^3} = r^{2/5} \times \frac{r^3}{dr}
\]

### Step 3: Simplify the resulting expression

Now, multiply the terms:

\[
r^{2/5} \times \frac{r^3}{dr} = \frac{r^{2/5} \cdot r^3}{dr} = \frac{r^{2/5 + 3}}{dr}
\]

Add the exponents in the numerator:

\[
2/5 + 3 = 2/5 + \frac{15}{5} = \frac{2 + 15}{5} = \frac{17}{5}
\]

So, the expression simplifies to:

\[
\frac{r^{17/5}}{dr}
\]

### Final Answer:

\[
\frac{r^{17/5}}{dr}
\]

This is the simplified form of the given expression.

Would you like further details or have any questions?

Here are some related questions you might find interesting:
1. How do you handle operations involving different exponents?
2. Can you explain how to simplify expressions with fractional exponents?
3. What are the rules for dividing fractions in algebra?
4. How do you convert a complex fraction into a simpler form?
5. What does it mean to multiply by the reciprocal of a fraction?

**Tip:** When dividing fractions, always remember that division by a fraction is the same as multiplying by its reciprocal.

Learn how to simplify the expression r^(7/5) / r ÷ dr / r^3 step-by-step with detailed explanations. This problem involves fractional exponents and dividing fractions in algebra. Suitable for students in Grades 9-12.

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