Algebra Examples

$(3 a b^{2}) {(3 a b)}^{2}$

Step 1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.1

Apply the product rule to $3 a b$ .

$3 a b^{2} ({(3 a)}^{2} b^{2})$

Step 1.2

Apply the product rule to $3 a$ .

$3 a b^{2} (3^{2} a^{2} b^{2})$

Step 2

Multiply $3$ by $3^{2}$ by adding the exponents.

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Step 2.1

Move $3^{2}$ .

$3^{2} \cdot 3 a b^{2} (a^{2} b^{2})$

Step 2.2

Multiply $3^{2}$ by $3$ .

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Step 2.2.1

Raise $3$ to the power of $1$ .

$3^{2} \cdot 3^{1} a b^{2} (a^{2} b^{2})$

Step 2.2.2

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

$3^{2 + 1} a b^{2} (a^{2} b^{2})$

Step 2.3

Add $2$ and $1$ .

$3^{3} a b^{2} (a^{2} b^{2})$

Step 3

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

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Step 3.1

Move $a^{2}$ .

$3^{3} (a^{2} a) b^{2} b^{2}$

Step 3.2

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

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Step 3.2.1

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

$3^{3} (a^{2} a^{1}) b^{2} b^{2}$

Step 3.2.2

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

$3^{3} a^{2 + 1} b^{2} b^{2}$

Step 3.3

Add $2$ and $1$ .

$3^{3} a^{3} b^{2} b^{2}$

Step 4

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

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Step 4.1

Move $b^{2}$ .

$3^{3} a^{3} (b^{2} b^{2})$

Step 4.2

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

$3^{3} a^{3} b^{2 + 2}$

Step 4.3

Add $2$ and $2$ .

$3^{3} a^{3} b^{4}$

Step 5

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

$27 a^{3} b^{4}$