Question

Miguel writes the expression 2nto the fourth. He says that when you double the value of n you double the value of the expression. Do you agree or disagree?

Answer 1

Miguel is incorrect, as doubling n in the expression 2n to the fourth power will result in the value of the expression becoming sixteen times greater, not double.

Step-by-step explanation:

I disagree with Miguel's statement that doubling the value of n in the expression 2n to the fourth power will only double the value of the expression. If we double the value of n, since n is raised to the fourth power, the overall expression's value increases by a factor of 24, which is sixteen. Therefore, the correct statement should be that when you double the value of n, the value of the expression will become sixteen times its original value.

Answer 2

Miguel's statement is not correct that when you double the value of n, you double the value of the expression 2n to the fourth.

Let me explain why step by step:

1. The expression is 2n to the fourth, which can be written as
`\(2n^4\).`

2. Doubling the value of n means changing it to 2n.

3. When you substitute 2n into the expression, you get
`\(2(2n)^4\)`, which simplifies to
`\(2(16n^4)\) or \(32n^4\).`

4. So, by doubling the value of n, you actually quadruple (multiply by 4) the value of the expression, not double it.

Therefore, doubling the value of n results in a value that is four times greater for the expression
`\(2n^4\),`so Miguel's statement is not correct.