which expression is equivalent to -8?\n-2^{-3}\n(-\\frac{1}{2})^{-3}\n(\\frac{1}{2})^{-3}\n2^{-3}

which expression is equivalent to -8?\n-2^{-3}\n(-\\frac{1}{2})^{-3}\n(\\frac{1}{2})^{-3}\n2^{-3}

which expression is equivalent to -8?\n-2^{-3}\n(-\\frac{1}{2})^{-3}\n(\\frac{1}{2})^{-3}\n2^{-3}

Answer

Explanation:

Step1: Recall negative - exponent rule

The negative - exponent rule is $a^{-n}=\frac{1}{a^{n}}$ for $a\neq0$ and $n\in\mathbb{Z}$.

Step2: Evaluate $-2^{-3}$

Using the negative - exponent rule, $2^{-3}=\frac{1}{2^{3}}=\frac{1}{8}$, so $-2^{-3}=-\frac{1}{8}$.

Step3: Evaluate $\left(-\frac{1}{2}\right)^{-3}$

By the negative - exponent rule, $\left(-\frac{1}{2}\right)^{-3}=\frac{1}{\left(-\frac{1}{2}\right)^{3}}$. Since $\left(-\frac{1}{2}\right)^{3}=-\frac{1}{8}$, then $\frac{1}{\left(-\frac{1}{2}\right)^{3}}=-8$.

Step4: Evaluate $\left(\frac{1}{2}\right)^{-3}$

Using the negative - exponent rule, $\left(\frac{1}{2}\right)^{-3}=\frac{1}{\left(\frac{1}{2}\right)^{3}}$. And $\left(\frac{1}{2}\right)^{3}=\frac{1}{8}$, so $\frac{1}{\left(\frac{1}{2}\right)^{3}} = 8$.

Step5: Evaluate $2^{-3}$

By the negative - exponent rule, $2^{-3}=\frac{1}{2^{3}}=\frac{1}{8}$.

Answer:

$\left(-\frac{1}{2}\right)^{-3}$