Question

simplify. express your answer using a single exponent.
$(z^{5})^{-9}$

Explanation:

Step1: Recall exponent rule

For \((a^m)^n\), we use the power - of - a - power rule which states that \((a^m)^n=a^{m\times n}\). Here, \(a = z\), \(m = 5\) and \(n=- 9\).

Step2: Apply the rule

We multiply the exponents: \(5\times(-9)=- 45\). So, \((z^{5})^{-9}=z^{5\times(-9)} = z^{-45}\) (or if we consider positive exponents, \(z^{-45}=\frac{1}{z^{45}}\), but the problem asks for a single exponent, and \(z^{-45}\) is in the form of a single exponent).

Answer:

\(z^{-45}\) (or \(\frac{1}{z^{45}}\) is also correct, but \(z^{-45}\) is a single exponent form as required)