Basic Math Examples

$2 y^{5} \cdot (2 v) \cdot (5 v^{2} y^{7})$

Step 1

Multiply $y^{5}$ by $y^{7}$ by adding the exponents.

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Step 1.1

Move $y^{7}$ .

$2 (y^{7} y^{5}) \cdot (2 v) \cdot (5 v^{2})$

Step 1.2

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

$2 y^{7 + 5} \cdot (2 v) \cdot (5 v^{2})$

Step 1.3

Add $7$ and $5$ .

$2 y^{12} \cdot (2 v) \cdot (5 v^{2})$

Step 2

Multiply $v$ by $v^{2}$ by adding the exponents.

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Step 2.1

Move $v^{2}$ .

$2 y^{12} \cdot (2 (v^{2} v)) \cdot 5$

Step 2.2

Multiply $v^{2}$ by $v$ .

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Step 2.2.1

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

$2 y^{12} \cdot (2 (v^{2} v^{1})) \cdot 5$

Step 2.2.2

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

$2 y^{12} \cdot (2 v^{2 + 1}) \cdot 5$

Step 2.3

Add $2$ and $1$ .

$2 y^{12} \cdot (2 v^{3}) \cdot 5$

Step 3

Rewrite using the commutative property of multiplication.

$2 \cdot 2 y^{12} v^{3} \cdot 5$

Step 4

Multiply $2$ by $2$ .

$4 y^{12} v^{3} \cdot 5$

Step 5

Multiply $5$ by $4$ .

$20 y^{12} v^{3}$