Question

selected response: 1 point for correct answer only
simplify: $(t^{-2})^{6}$
\\(\circ\\) $t^{12}$
\\(\circ\\) $\frac{t}{12}$
\\(\circ\\) $\frac{1}{t^{12}}$\\(\circ\\) $\frac{1}{t^{54}}$

Explanation:

Step1: Apply power of a power rule

To simplify \((t^{-2})^{6}\), we use the power of a power rule, which states that \((a^m)^n = a^{m\times n}\). Here, \(a = t\), \(m=-2\), and \(n = 6\). So we multiply the exponents: \(-2\times6=- 12\). Thus, \((t^{-2})^{6}=t^{-12}\).

Step2: Convert negative exponent to positive

Recall that \(a^{-n}=\frac{1}{a^{n}}\) for any non - zero number \(a\) and positive integer \(n\). So, \(t^{-12}=\frac{1}{t^{12}}\).

Answer:

\(\frac{1}{t^{12}}\) (corresponding to the option \(\frac{1}{t^{12}}\))