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The image contains four math problems under the section "Concept Builder 2." Here are the problems and their solutions:

### 1. Solve the following equations according to the instructions.  
1. **Is the equation \( 5^x \cdot 5^y = 5^{12} \) correct?**
   - Since the equation involves multiplication of exponents with the same base (5), you can add the exponents:
     \[
     5^x \cdot 5^y = 5^{x + y}
     \]
     For this to equal \( 5^{12} \), we must have:
     \[
     x + y = 12
     \]
     Therefore, the equation is correct as long as \( x + y = 12 \).

2. **Find the value of \( x \) for \( 2^{x+2} = 2^5 \cdot 2^3 \).**
   - Again, with the same base, you add the exponents:
     \[
     2^5 \cdot 2^3 = 2^{5+3} = 2^8
     \]
     Thus, the equation becomes:
     \[
     2^{x+2} = 2^8
     \]
     Since the bases are equal, we can equate the exponents:
     \[
     x + 2 = 8
     \]
     Solving for \( x \):
     \[
     x = 6
     \]

3. **Find the value of the expression \( \frac{729}{27} \div \frac{125}{25} \).**
   - Start by simplifying each fraction:
     \[
     \frac{729}{27} = 27 \quad \text{and} \quad \frac{125}{25} = 5
     \]
     So the expression becomes:
     \[
     27 \div 5 = \frac{27}{5} = 5.4
     \]

4. **If \( 1 + x + y = \frac{a}{b} \) then find the value of \( \frac{a}{b} \).**
   - The image is partially cut off, so it is unclear whether there are specific values given for \( x \) and \( y \). But in a generic sense:
     \[
     1 + x + y = \frac{a}{b}
     \]
     without specific values, \( \frac{a}{b} \) is simply \( 1 + x + y \).

Would you like to explore any specific problem in more detail or have any other questions?

Here are five related questions to think about:
1. What happens to the exponents when the bases are different but the operation is the same?
2. How would the equation change if \( 5^x \cdot 5^y \) was equal to \( 125^{12} \)?
3. Can you simplify \( 2^{x+3} = 2^7 \cdot 2^{-2} \) and solve for \( x \)?
4. How do you handle division of fractions like \( \frac{729/125}{27/25} \)?
5. How would you find \( x \) and \( y \) if \( \frac{a}{b} \) is given as a specific value?

**Tip:** When dealing with exponents, always try to simplify the expression by combining like terms before solving. This often makes the problem much easier to handle!

Solve the following equations according to the instructions: 1. Is the equation 5^x * 5^y = 5^12 correct? 2. Find the value of x for 2^{x+2} = 2^5 * 2^3. 3. Find the value of the expression 729/27 ÷ 125/25. 4. If 1 + x + y = a/b, then find the value of a/b.

This problem set involves solving exponential equations by applying the laws of exponents, finding the value of expressions with fractions, and simplifying complex fractions. Detailed solutions are provided to guide students through each step. Suitable for Grades 8-10.

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