Final answer:
If ( x ≠ 0 ), the expression x^(5/6) is equivalent to this expression [4√x³/x^(1/12)]. To simplify the expression 4√x³/x1/12, we express all terms using fractional exponents and combine them by subtraction since we are dividing, resulting in the expression x17/12 which simplifies to x5/6 (Option B).
Step-by-step explanation:
To find the expression equivalent to 4√x³/x1/12 given that x ≠ 0,
we should simplify the expression by combining the exponents according to the laws of exponents.
First, let's express the term 4√x³ with fractional exponents: 4 · x3/2.
Here, the 4 is equivalent to x0, since any non-zero number to the power of zero is 1.
Using this fact, we can write the entire expression as x0 · x3/2 divided by x1/12. Using the rule for dividing powers with the same base (A.9),
we subtract the exponents: 0 + 3/2 - 1/12.
To subtract these, we need a common denominator, which is 12 in this case, thus converting the exponents we get 0/12 + 18/12 - 1/12 = 17/12.
Therefore, the simplified expression is x17/12 which can be simplified to x15/6.
Therefore, (Option B), x5/6, is the correct answer.