Algebra Examples

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

Step 1

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

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Step 1.1

Move $k^{8}$ .

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

Step 1.2

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

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Step 1.2.1

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

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

Step 1.2.2

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

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

Step 1.3

Add $8$ and $1$ .

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

Step 2

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

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Step 2.1

Move $d$ .

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

Step 2.2

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

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Step 2.2.1

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

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

Step 2.2.2

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

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

Step 2.3

Add $1$ and $8$ .

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

Step 3

Apply the product rule to $k d$ .

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

Step 4

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

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Step 4.1

Move $k^{8}$ .

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

Step 4.2

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

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

Step 4.3

Add $8$ and $9$ .

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

Step 5

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

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Step 5.1

Move $d^{8}$ .

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

Step 5.2

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

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

Step 5.3

Add $8$ and $9$ .

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