which expression is equivalent to $4^{-1} \\times \\left(4^{-3}\\right)^{-1}$? \nanswer \n$\\frac{1}{64}$…
which expression is equivalent to $4^{-1} \\times \\left(4^{-3}\\right)^{-1}$? \nanswer \n$\\frac{1}{64}$ $16$ \n$4$ $\\frac{1}{16}$
Answer
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)