Precalculus Examples

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

Step 1

Multiply $x^{2}$ by $x^{5}$ by adding the exponents.

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Step 1.1

Move $x^{5}$ .

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

Step 1.2

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

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

Step 1.3

Add $5$ and $2$ .

$4 x^{7} y^{4} (2 y)$

Step 2

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

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Step 2.1

Move $y$ .

$4 x^{7} (y \cdot y^{4}) \cdot 2$

Step 2.2

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

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Step 2.2.1

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

$4 x^{7} (y^{1} y^{4}) \cdot 2$

Step 2.2.2

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

$4 x^{7} y^{1 + 4} \cdot 2$

Step 2.3

Add $1$ and $4$ .

$4 x^{7} y^{5} \cdot 2$

Step 3

Multiply $2$ by $4$ .

$8 x^{7} y^{5}$