Algebra Examples

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

Step 1

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

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Step 1.1

Move $x$ .

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

Step 1.2

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

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Step 1.2.1

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

$2 (x^{1} x^{3}) y (5 y^{2}) (3 x y)$

Step 1.2.2

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

$2 x^{1 + 3} y (5 y^{2}) (3 x y)$

Step 1.3

Add $1$ and $3$ .

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

Step 2

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

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Step 2.1

Move $x$ .

$2 (x \cdot x^{4}) y (5 y^{2}) (3 y)$

Step 2.2

Multiply $x$ by $x^{4}$ .

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Step 2.2.1

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

$2 (x^{1} x^{4}) y (5 y^{2}) (3 y)$

Step 2.2.2

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

$2 x^{1 + 4} y (5 y^{2}) (3 y)$

Step 2.3

Add $1$ and $4$ .

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

Step 3

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

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Step 3.1

Move $y^{2}$ .

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

Step 3.2

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

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Step 3.2.1

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

$2 x^{5} (y^{2} y^{1}) \cdot 5 (3 y)$

Step 3.2.2

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

$2 x^{5} y^{2 + 1} \cdot 5 (3 y)$

Step 3.3

Add $2$ and $1$ .

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

Step 4

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

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Step 4.1

Move $y$ .

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

Step 4.2

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

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Step 4.2.1

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

$2 x^{5} (y^{1} y^{3}) \cdot 5 \cdot 3$

Step 4.2.2

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

$2 x^{5} y^{1 + 3} \cdot 5 \cdot 3$

Step 4.3

Add $1$ and $3$ .

$2 x^{5} y^{4} \cdot 5 \cdot 3$

Step 5

Multiply $5$ by $2$ .

$10 x^{5} y^{4} \cdot 3$

Step 6

Multiply $3$ by $10$ .

$30 x^{5} y^{4}$