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)

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

164
Start Fraction 1 over 64 end fraction

604−3
Start Fraction 60 over 4 negative cubed end fraction

64
64

1⋅4−3

Answer 1

Start Fraction 1 over 64 end fraction

Answer 2

To simplify the given expression using the properties of integer exponents, we can follow these steps:

Step 1: Evaluate the exponent first: 47 = 16.

Step 2: Substitute the evaluated exponent back into the expression to get:
(15 - 3 * 16)04 - 3

Step 3: Simplify the multiplication: 3 * 16 = 48. Substitute the result into the expression:
(15 - 48)04 - 3

Step 4: Simplify the subtraction: 15 - 48 = -33. Substitute the result into the expression:
(-33)04 - 3

Step 5: Simplify the power of the base 04: 04 = 1. Substitute the result into the expression:
(-33)1 - 3

Step 6: Simplify the power of -33 to 1: -33^1 = -33. Substitute the result into the expression:
-33 - 3

Step 7: Simplify the subtraction: -33 - 3 = -36.

Therefore, the equivalent expression is -36.

Answer 3

To find the equivalent expression to (15 - 3 * 47)04 - 3 using the properties of integer exponents, we need to simplify the expression step by step.

First, let's simplify the expression within the parentheses:
(15 - 3 * 47) = (15 - 141) = -126

Next, let's simplify the exponent -3:
(04 - 3) = 0 - 3 = -3

Now we can write the simplified expression:
(-126)0 - 3

According to the properties of integer exponents, any number raised to the power of 0 is equal to 1. So, we can substitute 0 with 1 in the expression:
(-126)1 - 3

Negative exponents can be rewritten as the reciprocal of the base with positive exponents. So:
(-126)1 - 3 = 1/(-126)3

Finally, let's write the answer in a simplified form:
1/(-126)3 = 1/(-126 * -126 * -126) = 1/(-2,000,376)

Therefore, the equivalent expression to (15 - 3 * 47)04 - 3, using the properties of integer exponents, is 1/(-2,000,376) (or equivalently, -1/2,000,376). None of the given choices match this answer, so none of the options provided is correct.