https://file.aiquickdraw.com/mathbot/file/17293448000434atqvncr.jpg

The given expression is:

\[
\left( 8^{-1} - 9^{-1} \right)^{-1} \div \left( 4^{-1} - 9^{-1} \right)^{-1}
\]

### Step-by-step Solution:

1. **Simplify the first term** \(\left( 8^{-1} - 9^{-1} \right)^{-1}\):
   - \( 8^{-1} = \frac{1}{8} \) and \( 9^{-1} = \frac{1}{9} \).
   - So, \( 8^{-1} - 9^{-1} = \frac{1}{8} - \frac{1}{9} \).
   - Find the common denominator: 
     \[
     \frac{1}{8} - \frac{1}{9} = \frac{9 - 8}{72} = \frac{1}{72}.
     \]
   - Now, \(\left( \frac{1}{72} \right)^{-1} = 72\).

2. **Simplify the second term** \(\left( 4^{-1} - 9^{-1} \right)^{-1}\):
   - \( 4^{-1} = \frac{1}{4} \) and \( 9^{-1} = \frac{1}{9} \).
   - So, \( 4^{-1} - 9^{-1} = \frac{1}{4} - \frac{1}{9} \).
   - Find the common denominator:
     \[
     \frac{1}{4} - \frac{1}{9} = \frac{9 - 4}{36} = \frac{5}{36}.
     \]
   - Now, \(\left( \frac{5}{36} \right)^{-1} = \frac{36}{5}\).

3. **Divide the two results**:
   - The expression becomes:
     \[
     \frac{72}{\frac{36}{5}} = 72 \times \frac{5}{36} = 10.
     \]

So, the value of the expression is **10**.

Would you like more details or have any questions?

### Related questions:
1. How can you simplify expressions with negative exponents more efficiently?
2

The value of (8^-1 - 9^-1)^-1 ÷ (4^-1 - 9^-1)^-1?

Solve the expression (8^-1 - 9^-1)^-1 ÷ (4^-1 - 9^-1)^-1 step by step. Learn how to handle negative exponents and basic arithmetic operations. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation