Basic Math Examples

\sqrt{6 y} \cdot \sqrt{6 y}

$\sqrt{6 y} \cdot \sqrt{6 y}$

Step 1

Multiply

\sqrt{6 y} \sqrt{6 y}

$\sqrt{6 y} \sqrt{6 y}$ .

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Step 1.1

Raise

\sqrt{6 y}

$\sqrt{6 y}$ to the power of

1

$1$ .

{\sqrt{6 y}}^{1} \sqrt{6 y}

${\sqrt{6 y}}^{1} \sqrt{6 y}$

Step 1.2

Raise

\sqrt{6 y}

$\sqrt{6 y}$ to the power of

1

$1$ .

{\sqrt{6 y}}^{1} {\sqrt{6 y}}^{1}

${\sqrt{6 y}}^{1} {\sqrt{6 y}}^{1}$

Step 1.3

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

{\sqrt{6 y}}^{1 + 1}

${\sqrt{6 y}}^{1 + 1}$

Step 1.4

Add

1

$1$ and

1

$1$ .

{\sqrt{6 y}}^{2}

${\sqrt{6 y}}^{2}$

{\sqrt{6 y}}^{2}

${\sqrt{6 y}}^{2}$

Step 2

Rewrite

{\sqrt{6 y}}^{2}

${\sqrt{6 y}}^{2}$ as

6 y

$6 y$ .

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Step 2.1

Use

\sqrt[n]{a^{x}} = a^{\frac{x}{n}}

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

\sqrt{6 y}

$\sqrt{6 y}$ as

{(6 y)}^{\frac{1}{2}}

${(6 y)}^{\frac{1}{2}}$ .

{({(6 y)}^{\frac{1}{2}})}^{2}

${({(6 y)}^{\frac{1}{2}})}^{2}$

Step 2.2

Apply the power rule and multiply exponents,

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

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

{(6 y)}^{\frac{1}{2} \cdot 2}

${(6 y)}^{\frac{1}{2} \cdot 2}$

Step 2.3

Combine

\frac{1}{2}

$\frac{1}{2}$ and

2

$2$ .

{(6 y)}^{\frac{2}{2}}

${(6 y)}^{\frac{2}{2}}$

Step 2.4

Cancel the common factor of

2

$2$ .

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Step 2.4.1

Cancel the common factor.

${(6 y)}^{\frac{2}{2}}$

Step 2.4.2

Rewrite the expression.

${(6 y)}^{1}$

${(6 y)}^{1}$

Step 2.5

Simplify.

$6 y$

$6 y$

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