Simplify 4j^2k^6(2j^11)^3k^5

$4 j^{2} k^{6} {(2 j^{11})}^{3} k^{5}$

Multiply $k^{6}$ by $k^{5}$ by adding the exponents.

Move $k^{5}$ .

$4 j^{2} (k^{5} k^{6}) {(2 j^{11})}^{3}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 j^{2} k^{5 + 6} {(2 j^{11})}^{3}$

Add $5$ and $6$ .

$4 j^{2} k^{11} {(2 j^{11})}^{3}$

Apply the product rule to $2 j^{11}$ .

$4 j^{2} k^{11} (2^{3} {(j^{11})}^{3})$

Raise $2$ to the power of $3$ .

$4 j^{2} k^{11} (8 {(j^{11})}^{3})$

Multiply the exponents in ${(j^{11})}^{3}$ .

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

$4 j^{2} k^{11} (8 j^{11 \cdot 3})$

Multiply $11$ by $3$ .

$4 j^{2} k^{11} (8 j^{33})$

Multiply $j^{2}$ by $j^{33}$ by adding the exponents.

Move $j^{33}$ .

$4 (j^{33} j^{2}) k^{11} \cdot 8$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 j^{33 + 2} k^{11} \cdot 8$

Add $33$ and $2$ .

$4 j^{35} k^{11} \cdot 8$

Multiply $8$ by $4$ .

$32 j^{35} k^{11}$