Algebra Examples

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

Step 1

Rewrite using the commutative property of multiplication.

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

Step 2

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

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Step 2.1

Apply the product rule to $2 a b$ .

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

Step 2.2

Apply the product rule to $2 a$ .

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

Step 3

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

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Step 3.1

Move $a^{2}$ .

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

Step 3.2

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

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

Step 3.3

Add $2$ and $2$ .

$3 (2^{2} a^{4} b^{2}) b^{3}$

Step 4

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

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Step 4.1

Move $b^{3}$ .

$3 (2^{2} a^{4} (b^{3} b^{2}))$

Step 4.2

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

$3 (2^{2} a^{4} b^{3 + 2})$

Step 4.3

Add $3$ and $2$ .

$3 (2^{2} a^{4} b^{5})$

Step 5

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

$3 (4 a^{4} b^{5})$

Step 6

Multiply $4$ by $3$ .

$12 a^{4} b^{5}$