The expression \( 6 \cdot (2^{-5}) \) can be simplified as follows:

1. First, calculate the value of \( 2^{-5} \):
   \[
   2^{-5} = \frac{1}{2^5} = \frac{1}{32}
   \]

2. Now multiply this by 6:
   \[
   6 \cdot \frac{1}{32} = \frac{6}{32}
   \]

3. Simplify the fraction:
   \[
   \frac{6}{32} = \frac{3}{16}
   \]

So, \( 6 \cdot (2^{-5}) = \frac{3}{16} \).

Would you like more details or have any questions?

Here are 5 related questions you can explore:
1. How do you simplify powers of fractions with negative exponents?
2. What is \( 8^{-3} \cdot 4^2 \)?
3. How do you multiply fractions involving exponents?
4. What are the rules of exponents for multiplying two numbers?
5. What is the value of \( 6 \cdot 2^5 \)?

**Tip:** When dealing with negative exponents, remember that they represent the reciprocal of the base raised to the positive exponent.

This page explains how to simplify the expression 6 · 2^(-5). Learn step-by-step how negative exponents represent the reciprocal of the base and how to multiply fractions. This problem covers key concepts such as exponents, negative exponents, and fraction multiplication. Suitable for students in Grades 6-8.

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