Question

question
which expression is equivalent to $4^{4} \times \left(4^{-2}\
ight)^{4}$?
answer
$4^{-32}$ $4^{-3}$
$4^{-4}$ $4^{-2}$

Explanation:

Step1: Simplify the exponent of the second term

Using the power - of - a - power rule \((a^{m})^{n}=a^{m\times n}\), for \((4^{-2})^{4}\), we have \(m = - 2\) and \(n = 4\). So \((4^{-2})^{4}=4^{-2\times4}=4^{-8}\)

Step2: Multiply the two exponential terms

Using the product rule of exponents \(a^{m}\times a^{n}=a^{m + n}\), for \(4^{4}\times4^{-8}\), we have \(m = 4\) and \(n=-8\). Then \(4^{4}\times4^{-8}=4^{4+( - 8)}=4^{-4}\)

Answer:

\(4^{-4}\) (the option with \(4^{-4}\))