https://file.aiquickdraw.com/mathbot/file/1729516309582ckrdz9zm.jpg

The expression in the image is \( \frac{9^7}{9^2} \). To simplify it using the quotient rule of exponents, the rule states:

\[
\frac{a^m}{a^n} = a^{m-n}
\]

Here, \( a = 9 \), \( m = 7 \), and \( n = 2 \). So, applying the quotient rule:

\[
\frac{9^7}{9^2} = 9^{7-2} = 9^5
\]

Therefore, the correct answer is \( 9^5 \).

Would you like further explanation on how the quotient rule works or any other details?

Here are 5 related questions to deepen understanding:
1. How would you simplify \( \frac{9^8}{9^3} \)?
2. What happens if the exponents are negative, like \( \frac{9^{-2}}{9^{-5}} \)?
3. How does the quotient rule differ from the product rule of exponents?
4. What is the expanded form of \( 9^5 \)?
5. Can you use the quotient rule on variables instead of numbers, such as \( \frac{x^7}{x^2} \)?

**Tip:** When working with exponents, always pay attention to the base. The quotient rule applies only if the bases are the same.

Evaluate this expression using the quotient rule: 9^7 / 9^2.

Learn how to simplify the expression 9^7 / 9^2 using the quotient rule for exponents. This lesson covers key concepts in exponents and algebra, ideal for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation