https://file.aiquickdraw.com/mathbot/file/1725653846195awtw27lk.jpg

The image shows three math questions. I'll break them down and explain the solutions:

### **Question 48:**
\[
\frac{1}{(ab)} = \frac{1}{a} \cdot \frac{1}{b}
\]
- This is **true** because of the rule that \(\frac{1}{ab} = \frac{1}{a} \cdot \frac{1}{b}\), based on properties of fractions.

### **Question 49:**
\[
2^7 \cdot x^7 = (2x)^7
\]
- This is **true** because the property of exponents states that \((a^m \cdot b^m) = (ab)^m\).

### **Question 50:**
\[
a^4 \cdot a^4 = a^8
\]
- This is **true** since, by the exponent addition rule \(a^m \cdot a^n = a^{m+n}\), we add the exponents: \(4 + 4 = 8\).

Let me know if you want further explanations or have more questions!

### Here are five follow-up questions based on this:
1. What is the general rule for multiplying fractions with different denominators?
2. Can you explain the difference between multiplying exponents and raising a power to a power?
3. What happens when you divide exponents with the same base?
4. How would you simplify \((ab)^n\) when \(a\) and \(b\) are both variables?
5. How do you handle negative exponents in expressions like \((a^{-1} \cdot b^{-1})\)?

**Tip:** When working with exponents, always remember the basic rules such as product, quotient, and power rules. These will simplify many problems.

Three math questions involving fraction multiplication, exponent rules, and simplifying expressions.

Explore how to solve math problems involving fraction multiplication and exponent rules. This includes understanding properties of fractions and exponentiation rules, suitable for students in Grades 7-9.

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