https://file.aiquickdraw.com/mathbot/file/1726594726313hpias76s.jpg

The problem asks to find the value of:

\[
\left( \frac{1}{3-2} \right)^{-3}
\]

### Step-by-Step Solution:

1. **Simplify the denominator**:  
   \( 3 - 2 = 1 \)

   Now the expression becomes:

   \[
   \left( \frac{1}{1} \right)^{-3}
   \]

2. **Simplify the fraction**:  
   \( \frac{1}{1} = 1 \)

   So the expression simplifies to:

   \[
   1^{-3}
   \]

3. **Evaluate the exponent**:  
   Any number raised to any power will result in that number, so:

   \[
   1^{-3} = 1
   \]

Thus, the value of the expression is **1**.

Would you like any more details on this? 

Here are five related questions:
1. What is the result when a negative exponent is applied to a number?
2. How do you simplify expressions with exponents?
3. Can a fraction raised to a negative power ever result in a negative number?
4. How does changing the denominator in the original fraction affect the final result?
5. What are the general rules for evaluating expressions with zero exponents?

**Tip**: Remember that any number raised to the power of 0 is always 1, and \(1\) raised to any power remains \(1\)!

Learn how to simplify and solve the expression (1 / (3 - 2)) ^ (-3). This problem covers exponentiation and fraction simplification, using key exponent rules and concepts. Suitable 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