Question

Question 17
Use Structure Determine if the following numerical expressions are equivalent. Choose the correct answer and explanation.



[(110−2)0]3
and [(10−4)3]0


Multiple choice question.
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A)
They are not equivalent; One expression simplifies to 1106
and the other expression simplifies to 1.

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B)
They are equivalent; Both expressions simplify to 1.

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C)
They are equivalent; Both expression simplify to 0.

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D)
They are not equivalent; One expression simplifies to 106
and the other expression simplifies to 0.

Answer 1

To determine if the two numerical expressions \([(110−2)0]3\) and \([(10−4)3]0\) are equivalent, let's simplify each expression step by step.

1. **First Expression: \([(110−2)0]3\)**
- Calculate \(110 - 2\):
\[
110 - 2 = 108
\]
- The expression now is \([1080]3\). Any number raised to the power of 0 is 1:
\[
1080 = 1
\]
- Raising 1 to any power doesn't change its value:
\[
1^3 = 1
\]

2. **Second Expression: \([(10−4)3]0\)**
- Calculate \(10 - 4\):
\[
10 - 4 = 6
\]
- Raise 6 to the power of 3:
\[
6^3 = 216
\]
- Now, raise 216 to the power of 0:
\[
216^0 = 1
\]

Now, let's summarize the results:
- \([(110−2)0]3\) simplifies to 1.
- \([(10−4)3]0\) also simplifies to 1.

Since both expressions simplify to 1, the correct answer is:

**B) They are equivalent; Both expressions simplify to 1.**