Question

Which of the following is the equivalent expression to (15−3 ⋅ 47)04−3 that has been generated by applying the Properties of Integer Exponents?(1 point)

Responses

604−3
Start Fraction 60 over 4 negative cubed end fraction
164
Start Fraction 1 over 64 end fraction
1⋅4−3
1 times 4 negative cubed
64

Answer 1

[AI-generated answer — Bot GPT 3.5]

The correct equivalent expression is (1⋅4^(-3)) which simplifies to 1/64

Answer 2

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

2392
Start Fraction 2 cubed over 9 squared end fraction
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
23 ⋅92
2 cubed times 9 squared
2−7⋅9−129⋅9−10

Answer 3

[AI-generated answer — Bot GPT 3.5]

The correct equivalent expression is 2^(-7)⋅9^(-129)⋅9^(-10)

Answer 4

[AI-generated answer — Step-by-Step Bot]

To find the equivalent expression using the properties of integer exponents, follow these steps:

Step 1: Simplify the division inside the parentheses: 15 - 3 * 47 = 15 - 141 = -126.

Step 2: Apply the exponent -3 to -126: (-126)^(-3).

Step 3: The negative exponent can be rewritten as a positive exponent by taking the reciprocal of the base: (-126)^(-3) = 1/(-126)^3.

Step 4: Cubing the base, we have (-126)^3 = -126 * -126 * -126 = -2,003,496.

Step 5: Taking the reciprocal, we get 1/(-2,003,496) = -1/2,003,496.

Therefore, the equivalent expression is "-1/2,003,496", which is not among the given options.