Question

Question

Write in exponent form: 2x⋅2x⋅2x⋅2x
(1 point)
Responses

Because when you are multiplying with exponents, you would add to get 8⋅x4
Because when you are multiplying with exponents, you would add to get 8⋅x4

Because we only worry about the exponent on the variable, 2⋅x4
Because we only worry about the exponent on the variable, 2⋅x4

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, 24⋅x4

Answer 1

To write \( 2x \cdot 2x \cdot 2x \cdot 2x \) in exponent form, you can see that you have 4 factors of \( 2x \).

Using the property of exponents that states \( a^m \cdot a^n = a^{m+n} \), you can express \( 2x \) as \( (2^1 \cdot x^1) \) being multiplied 4 times.

So, you separately consider the factors:

1. For the coefficient \( 2 \): There are 4 factors of \( 2 \), which can be expressed as \( 2^4 \).
2. For the variable \( x \): There are 4 factors of \( x \), which can be expressed as \( x^4 \).

Thus, combining these, the expression in exponent form becomes:

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

The most appropriate response will be:

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