Question

raising a power to a power simplify ((10^{-2})^4). options: (-10^8), (-10^{-6}), (10^{-6}), (10^{-8})

Explanation:

Step1: Recall exponent rule

When raising a power to a power, we multiply the exponents: \((a^m)^n = a^{m\times n}\). Here, \(a = 10\), \(m=-2\), and \(n = 4\).

Step2: Apply the rule

Calculate the exponent: \(-2\times4=-8\). So, \((10^{-2})^4 = 10^{-8}\).

Answer:

\(10^{-8}\) (the first option among the given choices)