Algebra Examples

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

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

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

3 x^{2} y^{3}

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

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

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

Step 1.2

Apply the product rule to

3 x^{2}

$3 x^{2}$ .

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

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

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

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

Step 2

Raise

3

$3$ to the power of

3

$3$ .

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

$27 {(x^{2})}^{3} {(y^{3})}^{3}$

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}

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

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

$27 x^{2 \cdot 3} {(y^{3})}^{3}$

Step 3.2

Multiply

2

$2$ by

3

$3$ .

27 x^{6} {(y^{3})}^{3}

$27 x^{6} {(y^{3})}^{3}$

27 x^{6} {(y^{3})}^{3}

$27 x^{6} {(y^{3})}^{3}$

Step 4

Multiply the exponents in

{(y^{3})}^{3}

${(y^{3})}^{3}$ .

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Step 4.1

Apply the power rule and multiply exponents,

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

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

27 x^{6} y^{3 \cdot 3}

$27 x^{6} y^{3 \cdot 3}$

Step 4.2

Multiply

3

$3$ by

3

$3$ .

27 x^{6} y^{9}

$27 x^{6} y^{9}$

27 x^{6} y^{9}

$27 x^{6} y^{9}$

⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$