Precalculus Examples

(12 x^{3} y^{3}) (6 x^{4} y^{6})

$(12 x^{3} y^{3}) (6 x^{4} y^{6})$

Step 1

Multiply

x^{3}

$x^{3}$ by

x^{4}

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

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Step 1.1

Move

x^{4}

$x^{4}$ .

12 (x^{4} x^{3}) y^{3} (6 y^{6})

$12 (x^{4} x^{3}) y^{3} (6 y^{6})$

Step 1.2

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

12 x^{4 + 3} y^{3} (6 y^{6})

$12 x^{4 + 3} y^{3} (6 y^{6})$

Step 1.3

Add

4

$4$ and

3

$3$ .

12 x^{7} y^{3} (6 y^{6})

$12 x^{7} y^{3} (6 y^{6})$

12 x^{7} y^{3} (6 y^{6})

$12 x^{7} y^{3} (6 y^{6})$

Step 2

Multiply

y^{3}

$y^{3}$ by

y^{6}

$y^{6}$ by adding the exponents.

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Step 2.1

Move

y^{6}

$y^{6}$ .

12 x^{7} (y^{6} y^{3}) \cdot 6

$12 x^{7} (y^{6} y^{3}) \cdot 6$

Step 2.2

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

12 x^{7} y^{6 + 3} \cdot 6

$12 x^{7} y^{6 + 3} \cdot 6$

Step 2.3

Add

6

$6$ and

3

$3$ .

12 x^{7} y^{9} \cdot 6

$12 x^{7} y^{9} \cdot 6$

12 x^{7} y^{9} \cdot 6

$12 x^{7} y^{9} \cdot 6$

Step 3

Multiply

6

$6$ by

12

$12$ .

72 x^{7} y^{9}

$72 x^{7} y^{9}$

(12 x^{3} y^{3}) (6 x^{4} y^{6})

$(12 x^{3} y^{3}) (6 x^{4} y^{6})$

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[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$