Final answer:
None of the given options (1x/8, 3x/4, 6x/8, 8x/16) is equivalent to the expression 2³x - 4. Raising 2 to the third power gives us 8, making the correct expression 8x - 4, which is not reflected in the options provided.
Step-by-step explanation:
The question asks which expression is equivalent to 2³x - 4. To find an equivalent expression, we need to focus on the property that raising a number to a power, for example, 4³ which is equivalent to 4 × 4 × 4 in shorthand.
Thus, for 2³, we perform 2 × 2 × 2, which equals 8. Hence, 2³x is the same as 8x.
Now since we have 8x, we subtract 4 to get 8x - 4.
Looking at the options provided, none of them expresses 8x - 4 directly.
However, it is essential to note that division is the inverse operation of multiplication and that multiplying by a fraction is just another way of expressing division.
For example, dividing by 8 is the same as multiplying by 1/8, and multiplying by 1/2 is the same as dividing by 2.
The option that reflects this understanding is option 3) 6x/8, since 6x divided by 8 reduces to 3x/4 when simplified, which is not equivalent to the original expression 2³x - 4.
Therefore, the correct answer is not listed among the options provided, as none of the options correctly reduces to 8x - 4.