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The given mathematical expression is:

\[
\frac{(x^6 \cdot y^{-2} \cdot z^2)^3}{(x^{-2} \cdot y^3 \cdot z^{-2})^{-3}}
\]

We need to simplify this expression step by step.

### Step 1: Apply the power rule \((a^m)^n = a^{m \cdot n}\) to both the numerator and denominator.

#### Numerator:
\[
(x^6 \cdot y^{-2} \cdot z^2)^3 = x^{6 \cdot 3} \cdot y^{-2 \cdot 3} \cdot z^{2 \cdot 3} = x^{18} \cdot y^{-6} \cdot z^6
\]

#### Denominator:
\[
(x^{-2} \cdot y^3 \cdot z^{-2})^{-3} = x^{-2 \cdot (-3)} \cdot y^{3 \cdot (-3)} \cdot z^{-2 \cdot (-3)} = x^6 \cdot y^{-9} \cdot z^6
\]

### Step 2: Combine the simplified forms of the numerator and denominator.

Now the expression becomes:

\[
\frac{x^{18} \cdot y^{-6} \cdot z^6}{x^6 \cdot y^{-9} \cdot z^6}
\]

### Step 3: Simplify by using the quotient rule \(\frac{a^m}{a^n} = a^{m-n}\).

For \(x\):

\[
\frac{x^{18}}{x^6} = x^{18-6} = x^{12}
\]

For \(y\):

\[
\frac{y^{-6}}{y^{-9}} = y^{-6 - (-9)} = y^{-6 + 9} = y^3
\]

For \(z\):

\[
\frac{z^6}{z^6} = z^{6-6} = z^0 = 1
\]

### Step 4: Write the final simplified expression.

The simplified form of the given expression is:

\[
x^{12} \cdot y^3
\]

So, the answer is:

\[


Bentuk sederhana dari \frac{(x^6 \cdot y^{-2} \cdot z^2)^3}{(x^{-2} \cdot y^3 \cdot z^{-2})^{-3}} adalah ...

Simplify the algebraic expression \frac{(x^6 \cdot y^{-2} \cdot z^2)^3}{(x^{-2} \cdot y^3 \cdot z^{-2})^{-3}} by applying the power rule and the quotient rule for exponents. Follow a detailed step-by-step process suitable for high school students in Grades 10-12.

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