Question

which of the following expressions is equivalent to ((2x)^3)?
2(x)(x)(x)
(2x)(2x)(2x)
2x·3
2x + 2x + 2x

Explanation:

Step1: Recall exponent definition

An expression \(a^n\) means multiplying \(a\) by itself \(n\) times. For \((2x)^3\), \(a = 2x\) and \(n = 3\).

Step2: Apply the definition

So \((2x)^3=(2x)\times(2x)\times(2x)\), as we multiply \(2x\) three times.
Check other options:

• \(2(x)(x)(x)=2x^3\), not equal to \((2x)^3 = 8x^3\).
• \(2x\cdot3 = 6x\), not equivalent.
• \(2x + 2x + 2x=6x\), not equivalent.

Answer:

B. \((2x)(2x)(2x)\) (assuming the second option is labeled B, with the text \((2x)(2x)(2x)\))