https://file.aiquickdraw.com/mathbot/file/1724860687891fm6wzjom.jpg

The expression provided is:

\[
\frac{r^4}{2r^2 \cdot r}
\]

Let's simplify this step by step.

### Step 1: Simplify the denominator

First, simplify the denominator by combining the like terms:

\[
2r^2 \cdot r = 2r^{2+1} = 2r^3
\]

So the expression becomes:

\[
\frac{r^4}{2r^3}
\]

### Step 2: Apply the quotient rule for exponents

The quotient rule for exponents states that \(\frac{a^m}{a^n} = a^{m-n}\). Apply this to the expression:

\[
\frac{r^4}{r^3} = r^{4-3} = r^1 = r
\]

So the expression simplifies to:

\[
\frac{r}{2}
\]

### Final Answer

The simplified form of the expression is:

\[
\frac{r}{2}
\]

Would you like further details or have any other questions?

### Follow-Up Questions:
1. How do you simplify expressions involving both coefficients and variables?
2. What is the process for simplifying polynomials with multiple variables?
3. How can the quotient rule for exponents be applied to fractions?
4. Why is it important to simplify expressions before solving equations?
5. How do different exponent rules apply when the exponents are negative?

**Tip:** When simplifying expressions, always combine like terms and apply the quotient rule to reduce the complexity of the expression.

Learn how to simplify the expression (r^4)/(2r^2 * r) step-by-step with a detailed explanation. This problem covers key concepts in exponents and the quotient rule for exponents. Suitable for students in Grades 7-9.

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