Question

Which of the following is an equivalent expression to (2−3 ⋅93)−429 ⋅9−10
with only positive exponents, generated by applying the Properties of Integer Exponents?(1 point)
Responses

212⋅9−1229⋅9−10
Start fraction 2 superscript 12 baseline times 9 superscript negative 12 baseline over 2 superscript 9 baseline times 9 superscript negative 10 baseline end fraction

2392
Start Fraction 2 cubed over 9 squared end fraction

23 ⋅92
2 cubed times 9 squared

2−7⋅9−129⋅9−10

Answer 1

To rewrite the expression \( (2 - 3 \cdot 9^3) - 429 \cdot 9^{-10} \) in an equivalent form with only positive exponents, we start by simplifying the expression step by step.

1. Rewrite negative exponents as positive exponents:
- \( 9^{-10} = \frac{1}{9^{10}} \)

Now, we will go through each option provided and check if it can be derived from simplifying the given expression with positive exponents:

1. **Response 1: \( 2^{12} \cdot 9^{-12} \div (2^9 \cdot 9^{-10}) \)**
- This expression involves a division of exponents and does simplify but doesn't correspond with the original expression as no exponent transformations match. Plus, it retains negative exponents.

2. **Response 2: \( \frac{2^3}{9^2} \)**
- Simplifying this yields a straightforward expression but does not match the original expression.

3. **Response 3: \( 2^3 \cdot 9^2 \)**
- This is a positive exponent form but also bears no relation to the original form.

4. **Response 4: \( 2^{-7} \cdot 9^{-12} \cdot 9^{-10} \)**
- Similar to previous responses, contains negative exponents and does not provide positive equivalent.

From this breakdown, we need to check if any transformations yield a combination that strictly uses positive exponents. However, none of the choices accurately reframe the original into a simpler configuration with strictly positive exponents.

Please re-evaluate the main expression:
If the need arises to address each of these further or seek assistance on computation specifics for accurately determining your equivalent expression based off what I have approached is needed, please let me know!