Write in exponent form: 2x⋅2x⋅2x⋅2x

Question

(1 point)
Responses

Because these are like terms, we just add the coefficients to get 8x
Because these are like terms, we just add the coefficients to get 8 x

Because there are 4 factors of 2 and 4 factors of x, 2(4)⋅x(4)
Because there are 4 factors of 2 and 4 factors of x, 24⋅x4

Because we only worry about the exponent on the variable, 2⋅x(4)
Because we only worry about the exponent on the variable, 2⋅x4

Because when you are multiplying with exponents, you would add to get 8⋅x(4)

Answer 1

To express \(2x \cdot 2x \cdot 2x \cdot 2x\) in exponent form, we observe that:

• The base \(2\) appears \(4\) times. This can be represented as \(2^4\).
• The variable \(x\) also appears \(4\) times. This can be represented as \(x^4\).

Putting them together, we can write:

\[ 2x \cdot 2x \cdot 2x \cdot 2x = 2^4 \cdot x^4 \]

So the correct answer is:

Because there are 4 factors of 2 and 4 factors of x, \(2^4 \cdot x^4\).