To find the values of \( M \) and \( N \), let's evaluate each expression step by step.

1. **Evaluating \( M \)**:
   \[
   M = 2^{-5} \times (-0.100010)
   \]
   The term \( 2^{-5} \) can be rewritten as:
   \[
   2^{-5} = \frac{1}{2^5} = \frac{1}{32}
   \]
   Therefore:
   \[
   M = \frac{1}{32} \times (-0.100010)
   \]

   Calculating \( M \):
   \[
   M = \frac{-0.100010}{32} \approx -0.0031253
   \]

2. **Evaluating \( N \)**:
   \[
   N = 2^{-5} \times (-0.01111)
   \]
   Similarly, using \( 2^{-5} = \frac{1}{32} \):
   \[
   N = \frac{1}{32} \times (-0.01111)
   \]

   Calculating \( N \):
   \[
   N = \frac{-0.01111}{32} \approx -0.0003472
   \]

Therefore, the values are:
\[
M \approx -0.0031253
\]
\[
N \approx -0.0003472
\]

Would you like more details or have any questions?

Here are 5 questions you might want to ask:
1. How do you simplify expressions with negative exponents?
2. Can you explain the rules for multiplying decimals?
3. What is the process for converting between fractions and decimals?
4. How do you calculate powers of 2?
5. What are some tips for solving similar problems in algebra?

**Tip:** When working with negative exponents, remember that they represent the reciprocal of the base raised to the positive exponent. This can help simplify complex expressions step by step.

Learn how to evaluate expressions involving exponents and decimals with detailed step-by-step solutions. This problem covers evaluating expressions with negative exponents and multiplication of decimals. 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