Algebra Examples

$7 v^{3} \cdot 10 u^{3} v^{5} \cdot 8 u v^{3}$

Step 1

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

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Step 1.1

Move $v^{5}$ .

$7 (v^{5} v^{3}) \cdot (10 u^{3}) \cdot (8 u v^{3})$

Step 1.2

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

$7 v^{5 + 3} \cdot (10 u^{3}) \cdot (8 u v^{3})$

Step 1.3

Add $5$ and $3$ .

$7 v^{8} \cdot (10 u^{3}) \cdot (8 u v^{3})$

Step 2

Multiply $v^{8}$ by $v^{3}$ by adding the exponents.

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Step 2.1

Move $v^{3}$ .

$7 (v^{3} v^{8}) \cdot (10 u^{3}) \cdot (8 u)$

Step 2.2

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

$7 v^{3 + 8} \cdot (10 u^{3}) \cdot (8 u)$

Step 2.3

Add $3$ and $8$ .

$7 v^{11} \cdot (10 u^{3}) \cdot (8 u)$

Step 3

Multiply $u^{3}$ by $u$ by adding the exponents.

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Step 3.1

Move $u$ .

$7 v^{11} \cdot (10 (u \cdot u^{3})) \cdot 8$

Step 3.2

Multiply $u$ by $u^{3}$ .

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Step 3.2.1

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

$7 v^{11} \cdot (10 (u^{1} u^{3})) \cdot 8$

Step 3.2.2

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

$7 v^{11} \cdot (10 u^{1 + 3}) \cdot 8$

Step 3.3

Add $1$ and $3$ .

$7 v^{11} \cdot (10 u^{4}) \cdot 8$

Step 4

Rewrite using the commutative property of multiplication.

$7 \cdot 10 v^{11} u^{4} \cdot 8$

Step 5

Multiply $7$ by $10$ .

$70 v^{11} u^{4} \cdot 8$

Step 6

Multiply $8$ by $70$ .

$560 v^{11} u^{4}$