Algebra Examples

$(2 x^{2} y^{6} z^{5}) (5 x^{4} y^{5} z^{3})$

Step 1

Multiply $x^{2}$ by $x^{4}$ by adding the exponents.

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Step 1.1

Move $x^{4}$ .

$2 (x^{4} x^{2}) y^{6} z^{5} (5 y^{5} z^{3})$

Step 1.2

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

$2 x^{4 + 2} y^{6} z^{5} (5 y^{5} z^{3})$

Step 1.3

Add $4$ and $2$ .

$2 x^{6} y^{6} z^{5} (5 y^{5} z^{3})$

Step 2

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

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Step 2.1

Move $y^{5}$ .

$2 x^{6} (y^{5} y^{6}) z^{5} (5 z^{3})$

Step 2.2

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

$2 x^{6} y^{5 + 6} z^{5} (5 z^{3})$

Step 2.3

Add $5$ and $6$ .

$2 x^{6} y^{11} z^{5} (5 z^{3})$

Step 3

Multiply $z^{5}$ by $z^{3}$ by adding the exponents.

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Step 3.1

Move $z^{3}$ .

$2 x^{6} y^{11} (z^{3} z^{5}) \cdot 5$

Step 3.2

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

$2 x^{6} y^{11} z^{3 + 5} \cdot 5$

Step 3.3

Add $3$ and $5$ .

$2 x^{6} y^{11} z^{8} \cdot 5$

Step 4

Multiply $5$ by $2$ .

$10 x^{6} y^{11} z^{8}$