Algebra Examples

$(- 2 n^{6} y^{5}) (- 6 n^{3} y^{2}) {(n y)}^{3}$

Step 1

Multiply $n^{6}$ by $n^{3}$ by adding the exponents.

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Step 1.1

Move $n^{3}$ .

$- 2 (n^{3} n^{6}) y^{5} (- 6 y^{2}) {(n y)}^{3}$

Step 1.2

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

$- 2 n^{3 + 6} y^{5} (- 6 y^{2}) {(n y)}^{3}$

Step 1.3

Add $3$ and $6$ .

$- 2 n^{9} y^{5} (- 6 y^{2}) {(n y)}^{3}$

Step 2

Multiply $y^{5}$ by $y^{2}$ by adding the exponents.

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Step 2.1

Move $y^{2}$ .

$- 2 n^{9} (y^{2} y^{5}) \cdot - 6 {(n y)}^{3}$

Step 2.2

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

$- 2 n^{9} y^{2 + 5} \cdot - 6 {(n y)}^{3}$

Step 2.3

Add $2$ and $5$ .

$- 2 n^{9} y^{7} \cdot - 6 {(n y)}^{3}$

Step 3

Multiply $- 6$ by $- 2$ .

$12 n^{9} y^{7} {(n y)}^{3}$

Step 4

Apply the product rule to $n y$ .

$12 n^{9} y^{7} (n^{3} y^{3})$

Step 5

Multiply $n^{9}$ by $n^{3}$ by adding the exponents.

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Step 5.1

Move $n^{3}$ .

$12 (n^{3} n^{9}) y^{7} y^{3}$

Step 5.2

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

$12 n^{3 + 9} y^{7} y^{3}$

Step 5.3

Add $3$ and $9$ .

$12 n^{12} y^{7} y^{3}$

Step 6

Multiply $y^{7}$ by $y^{3}$ by adding the exponents.

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Step 6.1

Move $y^{3}$ .

$12 n^{12} (y^{3} y^{7})$

Step 6.2

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

$12 n^{12} y^{3 + 7}$

Step 6.3

Add $3$ and $7$ .

$12 n^{12} y^{10}$