https://file.aiquickdraw.com/mathbot/file/172515487724904o7aj0w.jpg

The equation in the image is:

\[
\frac{\text{kg} \cdot \text{m}}{\text{s}^2} = \frac{\text{m}^x}{\text{s}^x} \cdot \frac{\text{kg}^x}{\text{m}^3x}
\]

Let's break this down and solve for the values of \(x\) and \(y\).

First, let's simplify the right-hand side:

\[
\frac{\text{m}^x}{\text{s}^x} \cdot \frac{\text{kg}^x}{\text{m}^{3x}} = \frac{\text{kg}^x \cdot \text{m}^x}{\text{s}^x \cdot \text{m}^{3x}}
\]

Combining like terms, we get:

\[
\frac{\text{kg}^x \cdot \text{m}^{x - 3x}}{\text{s}^x} = \frac{\text{kg}^x \cdot \text{m}^{-2x}}{\text{s}^x}
\]

The left-hand side is already in terms of kg, m, and s:

\[
\frac{\text{kg} \cdot \text{m}}{\text{s}^2}
\]

Equating the powers of each unit:

1. For kg: \(x = 1\)
2. For m: \(-2x = 1 \implies -2(1) = 1 \implies x = 1\)
3. For s: \(-x = -2 \implies x = 2\)

So the values are \(x = 1\) and \(y = 2\).

Would you like more details or have any questions about this? 

### Related Questions:
1. How do you solve dimensional analysis problems in physics?
2. What are the SI units for different physical quantities?
3. How can dimensional analysis help in checking the correctness of equations?
4. How do exponents work when multiplying and dividing units?
5. What are some common mistakes when working with units in physics problems?

**Tip:** When dealing with unit conversions or dimensional analysis, always ensure that the units on both sides of an equation match perfectly. This helps verify the correctness of the relationship.

Understand and solve the dimensional analysis problem kgm/s²=mx/sx . Kgx/m³x. Learn how to equate units and solve for the values of x and y using dimensional analysis principles. Suitable for advanced physics students.

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