https://file.aiquickdraw.com/mathbot/file/1725579910278dp1pdjaz.jpg

The mathematical expression in the image is:

\[
\frac{6.4 \times 10^7}{1.6 \times 10^5}
\]

### Step-by-Step Solution:

1. **Simplify the Powers of 10:**
   - The expression has a power of 10 in both the numerator and denominator. We can simplify it by subtracting the exponents of the base 10.

   \[
   \frac{10^7}{10^5} = 10^{7-5} = 10^2
   \]

   So the expression simplifies to:

   \[
   \frac{6.4}{1.6} \times 10^2
   \]

2. **Simplify the Coefficients:**
   - Now, divide the coefficients \( 6.4 \) by \( 1.6 \):

   \[
   \frac{6.4}{1.6} = 4
   \]

3. **Final Expression:**
   - Now, multiply the simplified coefficient by the power of 10:

   \[
   4 \times 10^2 = 400
   \]

### Final Answer:
The value of the expression is \( 400 \).

---

Do you want details or have any questions?

Here are 5 related questions to explore further:
1. How would you solve this expression if the exponents were negative?
2. What happens if the base of the powers of 10 were different in the numerator and denominator?
3. Can you express \( 400 \) in scientific notation?
4. How does simplifying expressions with exponents differ if the bases are not the same?
5. How would you multiply or divide expressions with larger powers of 10?

**Tip:** When dealing with expressions involving powers of 10, remember to simplify by subtracting exponents if they are in a division format.

Simplify the mathematical expression: (6.4 × 10^7) ÷ (1.6 × 10^5).

Learn how to simplify the expression (6.4 × 10^7) ÷ (1.6 × 10^5) using the laws of exponents. This step-by-step guide will help students in Grades 9-11 understand exponent simplification and scientific notation.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation