Solve for x, where M is molar and s is seconds.
x = (2.8 × 103 M-2
• 5 1)(0.42 M)3
Enter the answer. Include units. Use the exponent key above the answer box to indicate any exponent on your units.

Let's solve the expression step by step. The expression given is:

\[
x = (2.8 \times 10^3 \, M^{-2} \cdot 5 \, \text{s}^{-1})(0.42 \, M)^3
\]

First, let's break it down:

1. **Simplify the multiplication inside the parentheses:**

\[
2.8 \times 10^3 \, M^{-2} \cdot 5 \, \text{s}^{-1} = (2.8 \times 5) \times 10^3 \, M^{-2} \, \text{s}^{-1}
\]

Calculating the numbers:

\[
2.8 \times 5 = 14
\]

So, the expression inside the parentheses becomes:

\[
14 \times 10^3 \, M^{-2} \, \text{s}^{-1} = 1.4 \times 10^4 \, M^{-2} \, \text{s}^{-1}
\]

2. **Calculate \((0.42 \, M)^3\):**

\[
(0.42 \, M)^3 = 0.42^3 \, M^3
\]

Calculate \(0.42^3\):

\[
0.42^3 = 0.074088
\]

So, 

\[
(0.42 \, M)^3 = 0.074088 \, M^3
\]

3. **Multiply both parts together:**

\[
x = (1.4 \times 10^4 \, M^{-2} \, \text{s}^{-1}) \times (0.074088 \, M^3)
\]

Multiply the numbers and combine the units:

\[
x = 1.4 \times 10^4 \times 0.074088 \, M^{-2 + 3} \, \text{s}^{-1}
\]

Calculating \(1.4 \times 10^4 \times 0.074088\):

\[
1.4 \times 10^4 \times 0.074088 = 1034.232
\]

Simplify the units:

\[
M^{-2 + 3} = M^1 = M
\]

So, the final expression for \(x\) is:

\[
x = 1034.232 \, M \, \text{s}^{-1}
\]

**Answer:**

\[
x = 1034.232 \, M \, \text{s}^{-1}
\]

### Would you like more details or have any questions? Here are some related questions:

1. How do you simplify expressions with multiple units?
2. What are the rules for multiplying and dividing powers in algebra?
3. How can units in a chemical equation affect the calculation of rates?
4. How do you handle large numbers and scientific notation in calculations?
5. What are some common errors to watch out for when working with units in chemistry?

**Tip:** When working with units, always keep track of each unit step-by-step to avoid mistakes and ensure the final result is dimensionally consistent.

Explore how to solve for x using units and scientific notation. This problem involves multiplication of units and calculating with scientific notation, providing a detailed step-by-step solution. Suitable for high school and above.

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