Question

What is the value of the expression simplified in Standard Notation: (3.2×10−2)(4.2×106)(5.2×105)
(1 point)
Responses

0.0026
0.0026

0.26
0.26

0.00026
0.00026

2.6

Answer 1

One answer

Answer 2

To simplify the expression \((3.2 \times 10^{-2})(4.2 \times 10^{6})(5.2 \times 10^{5})\), we can follow these steps:

1. **Multiply the coefficients:**
\[
3.2 \times 4.2 \times 5.2
\]
Calculate that step-by-step:
- \(3.2 \times 4.2 = 13.44\)
- Then \(13.44 \times 5.2 = 69.728\)

2. **Add the exponents of the powers of 10:**
\[
10^{-2} \times 10^{6} \times 10^{5} = 10^{-2 + 6 + 5} = 10^{9}
\]

3. **Combine the results:**
\[
69.728 \times 10^{9}
\]

4. **Convert to standard notation:**
To put it in standard notation, we need to express \(69.728\) as a number between \(1\) and \(10\). We do this by moving the decimal point one place to the left:
\[
69.728 = 6.9728 \times 10^1
\]
Therefore:
\[
69.728 \times 10^9 = 6.9728 \times 10^{1+9} = 6.9728 \times 10^{10}
\]

5. **Final Result:**
Since \(6.9728 \times 10^{10}\) is not listed in the answer choices, it's clear that I have miscalculated the expected outcome.

6. Instead, let's check **if I made a mistake in simplification:**

Let’s recalculate coefficient multiplication and ensure carefulness:
\[
3.2 \times 4.2 = 13.44
\]
\(13.44 \times 5.2\) confirms to \(69.728\).

Now, going back to exponent addition:
\[
-2 + 6 + 5 = 9 \rightarrow 10^9
\]

So, combining again:
\[
69.728 \times 10^9 = 6.9728 \times 10^{10}.
\]

At this junction, note:
\[
6.9728 \times 10^{10} =\text{Actual value is large. What really needed is a different perspective on expectations.}
\]

Check unit tests for small values... but none falsify.

I seem out from the answer choices specified.

### Conclusion
None of the provided options: \(0.0026\), \(0.26\), \(0.00026\), \(2.6\) match the scenario performed fully according to the operations elucidated.

My apologies for misunderstanding beginning values. Is anything particular which I may assist reflections for, or correct initial digit placement or values?