https://file.aiquickdraw.com/mathbot/file/1727226679673qf84o99g.jpg

The image you've uploaded contains a table discussing the division of exponents. It looks like a worksheet explaining how to simplify division problems involving powers, along with step-by-step explanations.

Here is an analysis of the table:

### Section 1 (Simplified Example):
- **Expression**: \( \frac{3^9}{3^4} \)
- **Solution**: \( \frac{3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3}{3 \times 3 \times 3 \times 3} \)
- This simplifies to \( 3^5 \), since you subtract the exponents: \( 9 - 4 = 5 \).
- **Final Form**: \( 3^5 \).

### Section 2:
- **Expression**: \( \frac{(-2)^6}{(-2)^3} \)
- **Solution**: Using the rule of subtracting exponents: \( (-2)^{6-3} = (-2)^3 \).
- **Final Form**: \( (-2)^3 \).

### Section 3 (Needs Completion):
- **Expression**: \( \frac{(4.2)^{10}}{(4.2)^5} \)
- **Solution**: Similarly, subtracting the exponents: \( (4.2)^{10-5} = (4.2)^5 \).
- **Final Form**: \( (4.2)^5 \).

### Section 4 (Needs Completion):
- **Expression**: \( \frac{2^7}{2^1} \)
- **Solution**: Subtracting exponents: \( 2^{7-1} = 2^6 \).
- **Final Form**: \( 2^6 \).

### General Rule:
At the bottom, it mentions the general rule of exponent division:
\[ \frac{a^m}{a^n} = a^{m-n} \]
This confirms the pattern of subtracting exponents when dividing powers of the same base.

Would you like further explanations on any specific part of this table? 

### Related Questions:
1. How do you handle exponent division when the base is negative?
2. What is the general rule for dividing two terms with exponents?
3. How would the rule change if the denominator has a negative exponent?
4. What is the result of dividing numbers with the same base and equal exponents?
5. How do you simplify complex exponents in fractions with different bases?

### Tip:
When dividing powers with the same base, always remember to subtract the exponent in the denominator from the exponent in the numerator.

Complete the table regarding the division of exponents, including simplifying the expressions.

Learn how to divide exponents and simplify expressions, including powers with negative bases. The step-by-step breakdown covers the exponent subtraction rule. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation