Question

select the equivalent expression.
\frac{1}{3} =?
choose 1 answer:
a \\ ((-1)^3
b \\ ((-3)^1

Explanation:

Step1: Evaluate the original expression

$\frac{1}{3} \approx 0.333$

Step2: Evaluate option A

$(-1)^3 = -1 \times -1 \times -1 = -1$

Step3: Evaluate option B

$(-3)^1 = -3$

Step4: Compare values

None of the options equal $\frac{1}{3}$, but if we assume a potential typo (e.g., the original expression was $-3$ or $-1$), but based on the given options, neither matches $\frac{1}{3}$. However, if we consider the problem might intend to ask for the equivalent of $3^{-1}$ which is $\frac{1}{3}$, but that is not listed. But strictly evaluating given options:

Step1: Calculate target value

$\frac{1}{3} \approx 0.333$

Step2: Calculate Option A

$(-1)^3 = -1$

Step3: Calculate Option B

$(-3)^1 = -3$

Step4: Match values

No option equals $\frac{1}{3}$

Answer:

None of the provided options are equivalent to $\frac{1}{3}$. If forced to choose from the given options, neither A nor B matches the value of $\frac{1}{3}$.

Wait, rechecking:
Wait, perhaps there was a formatting error. If the original question was $3^{-1}$, that equals $\frac{1}{3}$, but that's not an option. As per the given options:
$(-1)^3=-1$, $(-3)^1=-3$, neither equals $\frac{1}{3}$.

But if we follow the problem as stated, the answer is that no option is correct. But if we assume a mistake, but based on the given content: