Question

which expression is equivalent to ((4^{3})^{-1})? (\frac{1}{4^{-3}}) (\frac{1}{4^{3}}) (4^{3}) (4^{-4})

Explanation:

Step1: Recall exponent rule $(a^m)^n = a^{m\times n}$

For $(4^{3})^{-1}$, apply the rule: $4^{3\times(-1)} = 4^{-3}$

Step2: Recall negative exponent rule $a^{-n}=\frac{1}{a^{n}}$

Apply to $4^{-3}$: $\frac{1}{4^{3}}$

Answer:

$\frac{1}{4^{3}}$ (the second option)