https://file.aiquickdraw.com/mathbot/file/17258914627326mzjgf4g.jpg

The expression shown in the image is:

\[
\frac{5 \cdot 10^{-6} \cdot 10^6}{(10^2)^{-3}}
\]

Let's simplify this step by step:

1. Simplify the multiplication in the numerator:

   \[
   10^{-6} \cdot 10^6 = 10^{-6 + 6} = 10^0 = 1
   \]

   So, the expression becomes:

   \[
   \frac{5 \cdot 1}{(10^2)^{-3}}
   \]

2. Simplify the denominator:

   \[
   (10^2)^{-3} = 10^{2 \cdot (-3)} = 10^{-6}
   \]

   Now, the expression is:

   \[
   \frac{5}{10^{-6}}
   \]

3. When dividing by \(10^{-6}\), you can multiply by its reciprocal:

   \[
   \frac{5}{10^{-6}} = 5 \cdot 10^6
   \]

So, the simplified result is:

\[
5 \cdot 10^6
\]

Would you like more details, or do you have any questions about this solution?

Here are 5 related questions to explore further:

1. How do you simplify expressions with different bases?
2. What are the rules for exponent operations like addition, subtraction, multiplication, and division?
3. How do you handle negative exponents when simplifying expressions?
4. Can you convert \(5 \cdot 10^6\) into standard numerical form?
5. What happens if the exponents are not integers, such as fractions?

**Tip:** Always remember the rule \(a^{-n} = \frac{1}{a^n}\) when working with negative exponents.

Simplify the expression shown: 5·10^(-6)·10^6 divided by (10^2)^(-3)

Learn how to simplify the expression 5·10^(-6)·10^6 divided by (10^2)^(-3) step by step using exponentiation laws. Understand negative exponents and multiplication of powers. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation