Question

question
which expression is equivalent to ((6^{4})^{-1})?

answer
(6^{3}) (quad) (6^{-5})
(6^{-4}) (quad) (6^{4})

Explanation:

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

Here \(a = 6\), \(m = 4\), \(n=- 1\). So \((6^{4})^{-1}=6^{4\times(-1)}\)

Step2: Calculate the exponent

\(4\times(-1)=-4\), so \((6^{4})^{-1}=6^{-4}\)

Answer:

\(\boldsymbol{6^{-4}}\) (corresponding to the option with \(6^{-4}\))