Question

which expression is equivalent to $4^{-1} \times \left(4^{-3}\
ight)^{-1}$?
answer
$\frac{1}{64}$ $16$
$4$ $\frac{1}{16}$

Explanation:

Step1: Recall the power of a power rule: \((a^m)^n = a^{m\times n}\)

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

Step2: Recall the product of powers rule: \(a^m\times a^n = a^{m + n}\)

Now we have \(4^{-1}\times4^{3}\), apply the rule: \(4^{-1 + 3}=4^{2}\)

Step3: Calculate \(4^{2}\)

\(4^{2}=16\)

Answer:

16