To simplify the expression \(\left(\frac{2}{3}X\right)^3 : X^2\), let's follow the steps:

### Step 1: Simplify the cube
\[
\left(\frac{2}{3}X\right)^3 = \frac{2^3}{3^3}X^3 = \frac{8}{27}X^3
\]
So the expression becomes:
\[
\frac{8}{27}X^3 : X^2
\]

### Step 2: Division of terms
Now divide \(\frac{8}{27}X^3\) by \(X^2\):
\[
\frac{8}{27} \cdot \frac{X^3}{X^2} = \frac{8}{27} \cdot X = \frac{8}{27}X
\]

### Final result:
\[
\frac{8}{27}X
\]

Let me know if you'd like further details or have any questions.

Here are 5 related questions you can explore:
1. What is the result of \(\left(\frac{5}{2}X\right)^4 : X^3\)?
2. How do you simplify \(\left(\frac{4}{5}X\right)^2 : X\)?
3. How do you simplify the expression \(X^5 : X^2\)?
4. What is the cube of a fraction \(\frac{a}{b}\)?
5. How do you handle the division of variables with exponents?

**Tip:** When dividing variables with exponents, subtract the exponents (e.g., \(X^3 : X^2 = X^{3-2} = X\)).

This step-by-step guide simplifies the expression (2/3X)^3 : X^2. It covers key algebraic concepts like exponents, rational expressions, and the laws of exponents, making it perfect for students in Grades 8-10.

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