Evaluate 1/2(4k^5)^2

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

Simplify the expression.

Apply the product rule to $4 k^{5}$ .

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

Raise $4$ to the power of $2$ .

$\frac{1}{2} \cdot (16 {(k^{5})}^{2})$

Cancel the common factor of $2$ .

Factor $2$ out of $16 {(k^{5})}^{2}$ .

$\frac{1}{2} \cdot (2 (8 {(k^{5})}^{2}))$

Cancel the common factor.

$\frac{1}{2} \cdot (2 (8 {(k^{5})}^{2}))$

Rewrite the expression.

$8 {(k^{5})}^{2}$

Multiply the exponents in ${(k^{5})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$8 k^{5 \cdot 2}$

Multiply $5$ by $2$ .

$8 k^{10}$