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The given equation is:

\[
5 \times 5 \times 5 \times 5 \times 7 \times 7 = 5^x \times 7^y
\]

This simplifies as:

\[
5^4 \times 7^2 = 5^x \times 7^y
\]

From this, we can equate the powers of 5 and 7:

1. For the base 5: \( x = 4 \)
2. For the base 7: \( y = 2 \)

Thus, the correct values should be:
- \( x = 4 \)
- \( y = 2 \)

Let me know if you'd like more details or explanations!

### Related Questions:
1. What are the properties of exponents used in this problem?
2. How can you express \( 5^4 \times 7^2 \) in its expanded form?
3. Why is it valid to equate exponents when bases are the same?
4. What are the steps to simplify a product of powers with the same base?
5. How do we solve similar problems when there are more than two different prime bases?

### Tip:
When comparing powers, always ensure the bases are identical before equating the exponents.

Find the values of x and y: 5 × 5 × 5 × 5 × 7 × 7 = 5^x × 7^y

Learn how to solve for x and y in the equation 5 × 5 × 5 × 5 × 7 × 7 = 5^x × 7^y using the properties of exponents. This problem focuses on equating powers with the same base and is suitable for students in Grades 6-8.

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