Finite Math Examples

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

Step 1

Apply the product rule to $2 x^{2}$ .

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

Step 2

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

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Multiply $2$ by $2$ .

$4 x^{4} {(3 x^{3})}^{3}$

Step 4

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

$4 x^{4} (3^{3} {(x^{3})}^{3})$

Step 5

Rewrite using the commutative property of multiplication.

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

Step 6

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

$4 \cdot 27 x^{4} {(x^{3})}^{3}$

Step 7

Multiply $4$ by $27$ .

$108 x^{4} {(x^{3})}^{3}$

Step 8

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

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Step 8.1

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

$108 x^{4} x^{3 \cdot 3}$

Step 8.2

Multiply $3$ by $3$ .

$108 x^{4} x^{9}$

Step 9

Multiply $x^{4}$ by $x^{9}$ by adding the exponents.

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Step 9.1

Move $x^{9}$ .

$108 (x^{9} x^{4})$

Step 9.2

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

$108 x^{9 + 4}$

Step 9.3

Add $9$ and $4$ .

$108 x^{13}$