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Let's work through the expression to find its equivalent.

You are asked to simplify the expression:

\[
\frac{x^6 \cdot x^4}{x^{-4}}
\]

### Step-by-step solution:

1. **Simplify the numerator**: 
   \[
   x^6 \cdot x^4 = x^{6 + 4} = x^{10}
   \]
   (Using the rule \(x^a \cdot x^b = x^{a+b}\)).

2. **Simplify the entire expression**:
   Now we have:
   \[
   \frac{x^{10}}{x^{-4}}
   \]
   Applying the division rule of exponents, \( \frac{x^a}{x^b} = x^{a-b} \), we subtract the exponents:
   \[
   x^{10 - (-4)} = x^{10 + 4} = x^{14}
   \]

So, the simplified expression is:

\[
x^{14}
\]

### Correct Answer:
The equivalent expression is \(x^{14}\), so the correct choice is \(x^{14}\).

Let me know if you'd like further details or have any questions.

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Here are 5 related questions to expand your understanding:
1. How do you simplify \(\frac{x^7 \cdot x^3}{x^{-2}}\)?
2. What is the result of \(\frac{x^a \cdot x^b}{x^c}\)?
3. How do you simplify \(\frac{x^5}{x^2 \cdot x^3}\)?
4. How would you handle expressions with negative exponents in the numerator and denominator?
5. What is the value of \(\frac{2x^4 \cdot 3x^5}{x^{-2}}\)?

### Tip:
Always remember that when multiplying terms with the same base, you add the exponents, and when dividing, you subtract them.

Select the equivalent expression: \(\frac{x^6 \cdot x^4}{x^{-4}}\)

Discover how to simplify the exponential expression \(\frac{x^6 \cdot x^4}{x^{-4}}\) using the laws of exponents. This problem focuses on algebraic simplification techniques and is suitable for students in Grades 8-10.

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