We are tasked with simplifying the expression \((4 \times 10^{-5})^{-6}\).

### Step-by-Step Solution:

1. **Apply the exponent to both factors:**

   The expression can be broken into two parts:
   \[
   (4 \times 10^{-5})^{-6} = 4^{-6} \times (10^{-5})^{-6}
   \]

2. **Simplify each part:**
   - First, for \( 4^{-6} \):
     \[
     4^{-6} = \frac{1}{4^6} = \frac{1}{4096}
     \]
   
   - Next, for \( (10^{-5})^{-6} \):
     \[
     (10^{-5})^{-6} = 10^{-5 \times (-6)} = 10^{30}
     \]

3. **Combine the results:**
   Now, combine both parts:
   \[
   \frac{1}{4096} \times 10^{30} = \frac{10^{30}}{4096}
   \]

Thus, the simplified form of \((4 \times 10^{-5})^{-6}\) is:
\[
\frac{10^{30}}{4096}
\]

Let me know if you'd like further details!

---

Here are five related questions to deepen your understanding:
1. How do you simplify expressions with negative exponents?
2. What is the general rule for exponentiation of scientific notation?
3. How do you calculate \(4^{-6}\) step-by-step?
4. What is the meaning of scientific notation and when is it used?
5. Can you express \(\frac{10^{30}}{4096}\) in decimal form?

**Tip:** Always apply exponents to each part of the product separately before combining the results.

Learn how to simplify the expression (4 × 10^-5)^-6 step-by-step, applying the rules of exponents and scientific notation. This problem involves negative exponents and shows how to break down and combine factors. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation