Question

which expression is equivalent to ((5^{-1})^{-2})?
answer
(1) (\frac{1}{5})
(25) (125)

Explanation:

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

For \((5^{-1})^{-2}\), apply the rule: \(m = -1\), \(n = -2\), so it becomes \(5^{(-1)\times(-2)}\)

Step2: Calculate the exponent

\((-1)\times(-2)=2\), so the expression is \(5^2\)

Step3: Evaluate \(5^2\)

\(5^2 = 5\times5 = 25\)

Answer:

25