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)

Question

Responses

A. 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

B. 23 ⋅92
2 cubed times 9 squared

C. 2392
Start Fraction 2 cubed over 9 squared end fraction

D. 2−7⋅9−129⋅9−10
Start fraction 2 superscript negative 7 baseline times 9 superscript negative 1 baseline over 2 superscript 9 baseline times 9 superscript negative 10 baseline end fraction

Answer 1

To solve this problem, we can simplify the expression by applying the properties of integer exponents.

Starting with the given expression: (2−3⋅93)−429⋅9−10

First, we can simplify the exponent (2−3⋅93) by subtracting the exponents: 2−3 ⋅ 9^3 = 2−3 ⋅ 729

Then, we can simplify the exponent 429⋅9−10 by multiplying: 429 ⋅ 9−10 = 429 ⋅ (1/9^10)

The equivalent expression with positive exponents would be:
(2−3⋅93)−429⋅9−10 = 2−3 ⋅ 729 − 429 ⋅ (1/9^10)

Therefore, the correct answer is D. 2−7⋅9−129⋅9−10 (Start fraction 2 superscript negative 7 baseline times 9 superscript negative 1 baseline over 2 superscript 9 baseline times 9 superscript negative 10 baseline end fraction).