Question

which expression is equivalent to $(5^{-4})^{-5}$?
answer
$5^{-1}$
$5^{20}$
$5^{-0}$
$5^{16}$

Explanation:

Step1: Apply power - of - a - power rule

The power - of - a - power rule states that \((a^m)^n=a^{m\times n}\). For the expression \((5^{- 4})^{-5}\), where \(a = 5\), \(m=-4\) and \(n = - 5\), we have \((5^{-4})^{-5}=5^{(-4)\times(-5)}\).

Step2: Calculate the exponent

Multiply \(-4\) and \(-5\). Since \((-4)\times(-5)=20\), then \(5^{(-4)\times(-5)} = 5^{20}\).

Answer:

\(5^{20}\)