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.

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.