Question

simplify. express your answer using a single exponent. \\(\left(c^{-5}\
ight)^{2}\\)

Explanation:

Step1: Recall exponent power rule

The power of a power rule states that \((a^m)^n = a^{m\times n}\). Here, \(a = c\), \(m=-5\), and \(n = 2\).

Step2: Apply the rule

Substitute the values into the formula: \((c^{-5})^2=c^{-5\times2}\)
Calculate the exponent: \(-5\times2=-10\), so \((c^{-5})^2 = c^{-10}\)
We can also write this using positive exponents as \(\frac{1}{c^{10}}\), but since the problem allows a single exponent (including negative), \(c^{-10}\) is acceptable.

Answer:

\(c^{-10}\) (or \(\frac{1}{c^{10}}\))