Simplify (kd^8)(kd)^8(k^8d)

$(k d^{8}) {(k d)}^{8} (k^{8} d)$

Multiply $k$ by $k^{8}$ by adding the exponents.

Move $k^{8}$ .

$k^{8} k d^{8} {(k d)}^{8} d$

Multiply $k^{8}$ by $k$ .

Raise $k$ to the power of $1$ .

$k^{8} k^{1} d^{8} {(k d)}^{8} d$

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

$k^{8 + 1} d^{8} {(k d)}^{8} d$

Add $8$ and $1$ .

$k^{9} d^{8} {(k d)}^{8} d$

Multiply $d^{8}$ by $d$ by adding the exponents.

Move $d$ .

$k^{9} (d \cdot d^{8}) {(k d)}^{8}$

Multiply $d$ by $d^{8}$ .

Raise $d$ to the power of $1$ .

$k^{9} (d^{1} d^{8}) {(k d)}^{8}$

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

$k^{9} d^{1 + 8} {(k d)}^{8}$

Add $1$ and $8$ .

$k^{9} d^{9} {(k d)}^{8}$

Apply the product rule to $k d$ .

$k^{9} d^{9} (k^{8} d^{8})$

Multiply $k^{9}$ by $k^{8}$ by adding the exponents.

Move $k^{8}$ .

$k^{8} k^{9} d^{9} d^{8}$

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

$k^{8 + 9} d^{9} d^{8}$

Add $8$ and $9$ .

$k^{17} d^{9} d^{8}$

Multiply $d^{9}$ by $d^{8}$ by adding the exponents.

Move $d^{8}$ .

$k^{17} (d^{8} d^{9})$

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

$k^{17} d^{8 + 9}$

Add $8$ and $9$ .

$k^{17} d^{17}$