Theresa was asked to write an equivalent expression of

To follow Theresa's plan, we can start with a general expression that includes variables with exponents. For the sake of this example, let's use:

\( a^m \times a^n \times (a^p)^q \times a^{-r} \)

1. **Apply the Product of a Product Exponent Law**:
The Product of a Product Exponent Law states that when multiplying like bases, you add the exponents. Additionally, for the power of a power, you multiply the exponents. For the expression, we can group the first two terms together and the third term separately.

\( a^m \times a^n = a^{m+n} \)

So now we have:

\( a^{m+n} \times (a^p)^q \times a^{-r} \)

2. **Apply the Product of a Power Exponent Law**:
The Product of a Power Law states that when raising a power to a power, you multiply the exponents.

Applying this gives us:

\( a^{m+n} \times a^{p \cdot q} \times a^{-r} \)

3. **Combine all factors using the Product of Powers Law**:
This means we can now combine all the terms:

\( a^{(m+n) + (p \cdot q) - r} \)

4. **Use the Negative Exponent Law**:
The Negative Exponent Law states that \( a^{-x} = \frac{1}{a^x} \). If \( (m+n) + (p \cdot q) - r \) is negative, we can express it as:

\( \frac{1}{a^{-( (m+n) + (p \cdot q) - r )}} \) if necessary. However, we'll keep it as a positive exponent if already positive.

Thus, putting it all together according to Theresa's steps, we arrive at the final expression:

\( a^{(m+n) + (p \cdot q) - r} \)

If you have a specific expression to work with instead of the general form above, please provide that, and I'll apply the steps accordingly.