Questions: Simplify. Assume z ≠ 0. (z^(-6))^7

Solution Steps

To simplify the expression \((z^{-6})^{7}\), we can use the power of a power property of exponents, which states that \((a^m)^n = a^{m \cdot n}\). Applying this property, we multiply the exponents \(-6\) and \(7\).

To simplify the expression \((z^{-6})^{7}\), we use the power of a power property of exponents, which states that \((a^m)^n = a^{m \cdot n}\). Here, \(a = z\), \(m = -6\), and \(n = 7\).

Multiply the exponents \(-6\) and \(7\) to find the new exponent for \(z\): \[ -6 \times 7 = -42 \]

Final Answer