https://file.aiquickdraw.com/mathbot/file/17263605383706hg0lpc4.jpg

Let's evaluate each of the expressions given:

### a) \( 6^{-1} \)
- When you have a negative exponent, it means you take the reciprocal of the base. So:
  \[
  6^{-1} = \frac{1}{6}
  \]

### b) \( 4^{-2} \)
- Again, the negative exponent means you take the reciprocal of the base and then square it:
  \[
  4^{-2} = \frac{1}{4^2} = \frac{1}{16}
  \]

### c) \( 5^{-3} \)
- Similarly, take the reciprocal and cube the base:
  \[
  5^{-3} = \frac{1}{5^3} = \frac{1}{125}
  \]

Here are the answers:
- a) \( 6^{-1} = \frac{1}{6} \)
- b) \( 4^{-2} = \frac{1}{16} \)
- c) \( 5^{-3} = \frac{1}{125} \)

Would you like further explanations on any of these steps?

### Related Questions:
1. What is the general rule for negative exponents?
2. How does the rule for zero exponents differ from negative exponents?
3. Can you express \( x^{-n} \) for any base \( x \) and integer \( n \)?
4. How do you simplify expressions with both positive and negative exponents?
5. What happens when you multiply numbers with negative exponents?

**Tip:** When you see a negative exponent, always think of it as "moving the base to the denominator (if it's in the numerator) or to the numerator (if it's in the denominator) and making the exponent positive."

Evaluate each, giving the answer as a fraction or integer: a) 6^(-1) b) 4^(-2) c) 5^(-3)

Learn how to evaluate negative exponents with a detailed step-by-step solution for 6^(-1), 4^(-2), and 5^(-3). This lesson covers algebraic concepts and the laws of exponents. Suitable for 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