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
1⋅4^−3
64
60/4^−3
1/64
The equivalent expression is 1/64.
To find the equivalent expression generated by applying the Properties of Integer Exponents, let's break down the original expression step-by-step:
Step 1: Simplify the exponent expression inside the parentheses.
(15 − 3 ⋅ 47)^04 − 3
Step 2: Perform the multiplication.
(15 − 141)^04 − 3
Step 3: Simplify the subtraction.
(-126)^04 − 3
Step 4: Apply the Property of Integer Exponents.
((-126)^4)^−3
Step 5: Evaluate the base raised to the power of 4.
(20,376)^−3
Therefore, the correct equivalent expression, generated by applying the Properties of Integer Exponents, is:
1/ (20,376)^3
So the answer is 1/64 (option D).