Algebra Examples

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

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

Step 1

Use the power rule

{(a b)}^{n} = a^{n} b^{n}

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

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Step 1.1

Apply the product rule to

2 x^{2} y

$2 x^{2} y$ .

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

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

Step 1.2

Apply the product rule to

2 x^{2}

$2 x^{2}$ .

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

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

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

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

Step 2

Raise

2

$2$ to the power of

3

$3$ .

8 {(x^{2})}^{3} y^{3}

$8 {(x^{2})}^{3} y^{3}$

Step 3

Multiply the exponents in

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

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

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Step 3.1

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

8 x^{2 \cdot 3} y^{3}

$8 x^{2 \cdot 3} y^{3}$

Step 3.2

Multiply

2

$2$ by

3

$3$ .

8 x^{6} y^{3}

$8 x^{6} y^{3}$

8 x^{6} y^{3}

$8 x^{6} y^{3}$

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

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

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