https://file.aiquickdraw.com/mathbot/file/1724048891584c08cxqu3.jpg

The expression provided in the image is:

\[
5 \times 2^{-1} + 3 \times 2^{-2} + 2^{-3}
\]

Let's calculate each term step by step:

1. \( 2^{-1} = \frac{1}{2} = 0.5 \)
2. \( 2^{-2} = \frac{1}{4} = 0.25 \)
3. \( 2^{-3} = \frac{1}{8} = 0.125 \)

Now, multiplying these by their respective coefficients:

1. \( 5 \times 2^{-1} = 5 \times 0.5 = 2.5 \)
2. \( 3 \times 2^{-2} = 3 \times 0.25 = 0.75 \)
3. \( 2^{-3} = 0.125 \) (no coefficient to multiply here)

Adding these up:

\[
2.5 + 0.75 + 0.125 = 3.375
\]

So, the value of the expression is **3.375**.

Would you like more details or have any questions?

Here are some related questions:

1. How do you calculate the negative exponent of a fraction?
2. What is the significance of the coefficients in such an expression?
3. How would the result change if the exponents were positive instead of negative?
4. Can this expression be rewritten as a sum of fractions? If so, how?
5. What are some practical applications of expressions with negative exponents?

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

Learn how to calculate the expression 5 times 2 to the power of -1 plus 3 times 2 to the power of -2 plus 2 to the power of -3 with a step-by-step solution. This problem covers key concepts in exponents and arithmetic operations. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation