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The given expression is:

\[
(3x^{-1}y^3)^3 \cdot (-x^{-2}y^{-1})^2
\]

### Step 1: Simplify each part of the expression.

#### First term: \((3x^{-1}y^3)^3\)
Apply the power rule to each part:
\[
= 3^3 \cdot (x^{-1})^3 \cdot (y^3)^3 = 27 \cdot x^{-3} \cdot y^9
\]
So, \((3x^{-1}y^3)^3 = 27x^{-3}y^9\).

#### Second term: \((-x^{-2}y^{-1})^2\)
Again, apply the power rule to each part:
\[
= (-1)^2 \cdot (x^{-2})^2 \cdot (y^{-1})^2 = 1 \cdot x^{-4} \cdot y^{-2}
\]
So, \((-x^{-2}y^{-1})^2 = x^{-4}y^{-2}\).

### Step 2: Multiply the two simplified terms.

\[
(27x^{-3}y^9) \cdot (x^{-4}y^{-2}) = 27 \cdot x^{-3-4} \cdot y^{9-2} = 27x^{-7}y^7
\]

Thus, the simplified expression is:
\[
27x^{-7}y^7
\]

### Step 3: Rewriting with positive exponents:
\

Which expression is equivalent to (3x^{-1}y^3)^3(-x^{-2}y^{-1})^2?

Learn how to simplify the exponential expression (3x^{-1}y^3)^3(-x^{-2}y^{-1})^2 step by step. This algebra problem involves applying the power rule and the laws of exponents. Suitable for students in Grades 8-10.

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