https://file.aiquickdraw.com/mathbot/file/1726799487381c59hxbix.jpg

The given equation is:

\[
(a \times 10^b) \times (5.3 \times 10^8) = 2.226 \times 10^4
\]

We are tasked with finding the values of \(a\) and \(b\), knowing that \(a \times 10^b\) is in standard form.

### Steps to solve:

1. **Multiply the terms in standard form:**
   - First, express the equation by separating the powers of 10:
     \[
     (a \times 5.3) \times 10^{b+8} = 2.226 \times 10^4
     \]

2. **Equating the coefficients:**
   - From this, we can compare the coefficients of the numbers:
     \[
     a \times 5.3 = 2.226
     \]
   - Solving for \(a\):
     \[
     a = \frac{2.226}{5.3} \approx 0.42
     \]

3. **Equating the powers of 10:**
   - Now, equate the exponents:
     \[
     b + 8 = 4
     \]
   - Solving for \(b\):
     \[
     b = 4 - 8 = -4
     \]

### Final answer:
- \(a \approx 0.42\)
- \(b = -4\)

Would you like a more detailed explanation, or do you have any other questions?

Here are some related questions to deepen your understanding:

1. What is standard form and how is it used in scientific notation?
2. Why do we compare the coefficients and powers separately in such problems?
3. How would you handle a situation where \(a \times 10^b\) is not in standard form?
4. What are the implications of negative powers of 10 in scientific notation?
5. How can we use logarithms to simplify such exponential problems?

**Tip:** Always check if the coefficient \(a\) falls between 1 and 10 for the standard form to ensure correctness!

(a × 10^b) × (5.3 × 10^8) = 2.226 × 10^4. Given that a × 10^b is in standard form, work out the values of a and b.

Solve the equation (a × 10^b) × (5.3 × 10^8) = 2.226 × 10^4 to find the values of a and b. This problem involves scientific notation and exponent rules, suitable for students in Grades 9-11.

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