https://file.aiquickdraw.com/mathbot/file/1726024363360oilexn97.jpg

The expression given in the image is:

\[
\frac{x^6 \cdot x^4}{x^7}
\]

Let's simplify this step by step.

1. Apply the multiplication rule of exponents: \(x^a \cdot x^b = x^{a+b}\). So,

\[
x^6 \cdot x^4 = x^{6+4} = x^{10}
\]

2. Now, the expression becomes:

\[
\frac{x^{10}}{x^7}
\]

3. Use the division rule of exponents: \(\frac{x^a}{x^b} = x^{a-b}\). So,

\[
\frac{x^{10}}{x^7} = x^{10-7} = x^3
\]

Therefore, the equivalent expression is \(x^3\).

Among the answer choices, the correct option is **\(x^3\)**.

Would you like any further explanation or details on this?

Here are 5 related questions:
1. How do you simplify expressions with negative exponents?
2. What happens if you divide a number with the same exponent?
3. How do you simplify more complex exponential expressions with multiple terms?
4. Can you apply the same rules to expressions with fractional exponents?
5. How do you handle exponents when variables have coefficients?

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

Select the equivalent expression: (x^6 * x^4) / x^7

Learn how to simplify expressions with exponents using the multiplication and division rules. The problem (x^6 * x^4) / x^7 demonstrates how to apply exponent rules, such as x^a * x^b = x^(a+b) and x^a / x^b = x^(a-b), to reach the simplified expression x^3. This problem is suitable for Grades 7-9.

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