Precalculus Examples

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

Step 1

Multiply $x^{2}$ by $x^{4}$ by adding the exponents.

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Step 1.1

Move $x^{4}$ .

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

Step 1.2

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

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

Step 1.3

Add $4$ and $2$ .

$4 x^{6} {(3 x^{3})}^{2} \cdot 2$

Step 2

Apply the product rule to $3 x^{3}$ .

$4 x^{6} (3^{2} {(x^{3})}^{2}) \cdot 2$

Step 3

Rewrite using the commutative property of multiplication.

$4 \cdot 3^{2} x^{6} {(x^{3})}^{2} \cdot 2$

Step 4

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

$4 \cdot 9 x^{6} {(x^{3})}^{2} \cdot 2$

Step 5

Multiply $4$ by $9$ .

$36 x^{6} {(x^{3})}^{2} \cdot 2$

Step 6

Multiply the exponents in ${(x^{3})}^{2}$ .

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Step 6.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$36 x^{6} x^{3 \cdot 2} \cdot 2$

Step 6.2

Multiply $3$ by $2$ .

$36 x^{6} x^{6} \cdot 2$

Step 7

Multiply $x^{6}$ by $x^{6}$ by adding the exponents.

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Step 7.1

Move $x^{6}$ .

$36 (x^{6} x^{6}) \cdot 2$

Step 7.2

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

$36 x^{6 + 6} \cdot 2$

Step 7.3

Add $6$ and $6$ .

$36 x^{12} \cdot 2$

Step 8

Multiply $2$ by $36$ .

$72 x^{12}$