Algebra Examples

${(2 v)}^{2} \cdot (2 v^{2})$

Step 1

Rewrite using the commutative property of multiplication.

$2 {(2 v)}^{2} v^{2}$

Step 2

Apply the product rule to $2 v$ .

$2 (2^{2} v^{2}) v^{2}$

Step 3

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

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Step 3.1

Move $2^{2}$ .

$2^{2} \cdot 2 v^{2} v^{2}$

Step 3.2

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

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Step 3.2.1

Raise $2$ to the power of $1$ .

$2^{2} \cdot 2^{1} v^{2} v^{2}$

Step 3.2.2

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

$2^{2 + 1} v^{2} v^{2}$

Step 3.3

Add $2$ and $1$ .

$2^{3} v^{2} v^{2}$

Step 4

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

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Step 4.1

Move $v^{2}$ .

$2^{3} (v^{2} v^{2})$

Step 4.2

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

$2^{3} v^{2 + 2}$

Step 4.3

Add $2$ and $2$ .

$2^{3} v^{4}$

Step 5

Raise $2$ to the power of $3$ .

$8 v^{4}$