Question

1. \\(\frac{1}{2}(4k^5)^2\\)

Explanation:

Step1: Expand the squared term

Apply exponent rule $(ab)^n=a^n b^n$:
$(4k^5)^2 = 4^2 \cdot (k^5)^2 = 16k^{10}$

Step2: Multiply by the fraction

Multiply the result by $\frac{1}{2}$:
$\frac{1}{2} \cdot 16k^{10} = 8k^{10}$

Answer:

$8k^{10}$