Basic Math Examples

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

Step 1

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

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Step 1.1

Move $b^{2}$ .

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

Step 1.2

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

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Step 1.2.1

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

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

Step 1.2.2

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

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

Step 1.3

Add $2$ and $1$ .

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

Step 2

Apply the product rule to $a b$ .

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

Step 3

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

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Step 3.1

Move $a^{2}$ .

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

Step 3.2

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

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Step 3.2.1

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

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

Step 3.2.2

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

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

Step 3.3

Add $2$ and $1$ .

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

Step 4

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

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Step 4.1

Move $b^{2}$ .

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

Step 4.2

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

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

Step 4.3

Add $2$ and $3$ .

$2 a^{3} b^{5}$