Question

simplify. express your answer using a single exponent.
$(z^{-2})^{-6}$

Explanation:

Step1: Apply power of a power rule

When raising a power to a power, we multiply the exponents. The formula for \((a^m)^n\) is \(a^{m\times n}\). Here, \(a = z\), \(m=-2\), and \(n = -6\). So we calculate \((-2)\times(-6)\).
\((z^{-2})^{-6}=z^{(-2)\times(-6)}\)

Step2: Calculate the product of exponents

Multiply \(-2\) and \(-6\). \((-2)\times(-6) = 12\). So the expression simplifies to \(z^{12}\).

Answer:

\(z^{12}\)