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)
(15-3)04-3
To simplify the expression (15−3 ⋅ 47)04−3 using the properties of integer exponents, we can break it down step-by-step.
Step 1: Simplify the exponent 15−3 by applying the negative exponent rule, which states that a−n = 1/an. In this case, 15−3 = 1/15^3.
The expression becomes (1/15^3 ⋅ 47)04−3.
Step 2: Simplify the exponent 04−3 by applying the zero exponent rule, which states that any non-zero number raised to the power of 0 is equal to 1. In other words, any term with an exponent of 0 can be removed.
The expression becomes 1/15^3 ⋅ 47.
Therefore, the equivalent expression to (15−3 ⋅ 47)04−3, generated by applying the properties of integer exponents, is 1/15^3 ⋅ 47.
To determine the equivalent expression generated by applying the properties of integer exponents, we need to simplify the given expression step by step.
Let's break down the given expression:
1. Start with the term inside the parentheses: 15−3 ⋅ 47. This can be simplified by applying the rule that states when we have a negative exponent, we can move the base to the opposite side of the fraction and change the sign of the exponent. So, 15−3 can be rewritten as 1/15^3.
2. Now, let's substitute the simplified term back into the original expression: (1/15^3)04−3.
3. Evaluate the exponent 04. Any number raised to the power of 0 is equal to 1, so 04 is equal to 1.
4. Evaluate the exponent −3. To simplify the term, we know that a negative exponent can be rewritten as 1 over the number raised to the positive exponent: 1/15^3.
Finally, substitute the values back into the expression:
(1/15^3)1 = 1/15^3.
Therefore, the equivalent expression generated by applying the properties of integer exponents to the original expression (15−3 ⋅ 47)04−3 is 1/15^3.