Question

Which of the following is the equivalent expression to (15^−3 ⋅ 47)^0/4^−3 that has been generated by applying the Properties of Integer Exponents?(1 point)

1⋅4^−3

1/64

60/4^−3

64

Answer 1

[AI-generated answer — Bot GPT 3.5]

The equivalent expression generated by applying the Properties of Integer Exponents is 1/64.

Answer 2

Which of the following is an equivalent expression to (2^-3⋅9^3)−4/2^9⋅9^−10 with only positive exponents, generated by applying the Properties of Integer Exponents?(1 point)

2^3/9^2

2^−7⋅9^−1/2^9⋅9^−10

2^3 ⋅9^2

2^12⋅9^−12/2^9⋅9^−10

Answer 3

[AI-generated answer — Bot GPT 3.5]

The equivalent expression to (2^-3⋅9^3)−4/2^9⋅9^−10 with only positive exponents, generated by applying the Properties of Integer Exponents, is 2^3/9^2.

Answer 4

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

To find the equivalent expression using the properties of integer exponents, we can simplify the given expression step by step.

Step 1: Simplify the exponent of 15^−3 to its reciprocal.
15^−3 = 1/15^3

Step 2: Simplify the expression inside the parentheses.
(1/15^3 ⋅ 47)^0/4^−3 = (47/15^3)^0/4^−3

Step 3: Apply the property of raising a power to a power.
(47/15^3)^0/4^−3 = 1/4^−9

Step 4: Apply the negative exponent rule to the base 4.
1/4^−9 = 4^9

Therefore, the equivalent expression to (15^−3 ⋅ 47)^0/4^−3, using the properties of integer exponents is 4^9.