QuestionSolve for $x$ in the equation: $x=(8.4 \times 10^{3} M^{-2} \cdot s^{-1})(0.36 M)^{3}$ . Include units.

Studdy Solution

STEP 1

Assumptions1. The value of $x$ is calculated by multiplying $8.4 \times10^{3} M^{-} \cdot s^{-1}$ with $(0.36 M)^{3}$ . . The units of $x$ are derived from the units of the given quantities.

STEP 2

First, we need to calculate the value of $(0.36 M)^{}$ . This is done by cubing the value of $0.36 M$ .
$(0.36 M)^{} =0.36^{} M^{}$

STEP 3

Now, calculate the value of $0.36^{3}$ .
$0.36^{3} =0.046656$ So, $(0.36 M)^{3} =0.046656 M^{3}$ .

STEP 4

Now, we can calculate the value of $x$ by multiplying $8.4 \times10^{3} M^{-2} \cdot s^{-1}$ with $0.046656 M^{3}$ .
$x = (8.4 \times10^{3} M^{-2} \cdot s^{-1}) \times (0.046656 M^{3})$

STEP 5

Calculate the value of $x$ .
$x = (8.4 \times10^{3} M^{-2} \cdot s^{-1}) \times0.046656 M^{3} =391.9104 M \cdot s^{-1}$

STEP 6

The units of $x$ are derived from the units of the given quantities. The unit $M^{3}$ from $(0.36 M)^{3}$ cancels out with the $M^{-2}$ from $8.4 \times10^{3} M^{-2} \cdot s^{-1}$ , leaving the unit of $x$ as $M \cdot s^{-1}$ .
So, $x =391.9104 M \cdot s^{-1}$ .
The value of $x$ is $391.9104 M \cdot s^{-1}$ .

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