Algebra Examples

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

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 $2 x y$ .

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

Step 1.2

Apply the product rule to $2 x$ .

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

Step 2

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

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Step 2.1

Move $x^{2}$ .

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

Step 2.2

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

$2^{3} x^{2 + 3} y^{3} \cdot y^{2}$

Step 2.3

Add $2$ and $3$ .

$2^{3} x^{5} y^{3} \cdot y^{2}$

Step 3

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

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Step 3.1

Move $y^{2}$ .

$2^{3} x^{5} (y^{2} y^{3})$

Step 3.2

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

$2^{3} x^{5} y^{2 + 3}$

Step 3.3

Add $2$ and $3$ .

$2^{3} x^{5} y^{5}$

Step 4

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

$8 x^{5} y^{5}$