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The problem asks to identify expressions that are equivalent to \(7^7 \times 7^7\).

To solve this:

1. **Simplify the given expression**: \(7^7 \times 7^7\).
   - Using the property of exponents: \(a^m \times a^n = a^{m+n}\),
   - So, \(7^7 \times 7^7 = 7^{7+7} = 7^{14}\).

Now, let's evaluate each of the options:

- **Option 1: \(\frac{1}{7^{14}}\)** is equivalent to \(7^{-14}\), which is not equal to \(7^{14}\).
- **Option 2: \(7^{49}\)** is not equal to \(7^{14}\).
- **Option 3: \(\left(7^7\right)^2\)** can be simplified using the power of a power rule: \((a^m)^n = a^{m \times n}\), so \(\left(7^7\right)^2 = 7^{7 \times 2} = 7^{14}\).
- **Option 4: \(7^{14}\)** is exactly \(7^{14}\).

Thus, the correct expressions that are equivalent to \(7^7 \times 7^7\) are:

- \(\left(7^7\right)^2\)
- \(7^{14}\)

Would you like more details on exponent rules or any related questions? Here are five questions to explore further:

1. What are the different properties of exponents?
2. How do you simplify expressions involving exponents with different bases?
3. How would the answer change if the problem was \(7^7 \times 7^6\)?
4. How do you solve equations that involve exponents?
5. What is the difference between \(7^{-14}\) and \(7^{14}\)?

**Tip:** When multiplying terms with the same base, simply add the exponents to find the product.

Select all the expressions that are equivalent to 7^7 * 7^7.

Learn how to identify expressions that are equivalent to 7^7 * 7^7 by applying the properties of exponents. This problem is suitable for students in the 7th grade.

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