Simplify the following. Use the $$ { }^{\wedge} $$ symbol for the exponent if needed. $$ \left(2 x^{3} y^{-3}\right)\left(2 x^{-1} y^{3}\right) $$

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To simplify the expression $$ \left(2 x^{3} y^{-3}\right)\left(2 x^{-1} y^{3}\right) $$, follow these steps:

1. **Multiply the constants:**
   $$
   2 \times 2 = 4
   $$

2. **Multiply the $$ x $$ terms using the law of exponents $$ x^a \times x^b = x^{a+b} $$:**
   $$
   x^{3} \times x^{-1} = x^{3-1} = x^{2}
   $$

3. **Multiply the $$ y $$ terms:**
   $$
   y^{-3} \times y^{3} = y^{-3+3} = y^{0} = 1
   $$
   (Since any non-zero number raised to the power of 0 is 1.)

4. **Combine all the simplified parts:**
   $$
   4 \times x^{2} \times 1 = 4x^{2}
   $$

So, the simplified expression is:

$$
4x^{2}
$$
$$ 4x^{2} $$

Simplify the following. Use the \( { }^{\wedge} \) symbol for the exponent if needed. \( \left(2 x^{3} y^{-3}\right)\left(2 x^{-1} y^{3}\right) \)

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