Basic Math Examples

$\frac{1}{2} \cdot (12 \sqrt{3}) \cdot (6 \sqrt{3})$

Step 1

Cancel the common factor of $2$ .

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Step 1.1

Factor $2$ out of $12 \sqrt{3}$ .

$\frac{1}{2} \cdot (2 (6 \sqrt{3})) \cdot (6 \sqrt{3})$

Step 1.2

Cancel the common factor.

$\frac{1}{2} \cdot (2 (6 \sqrt{3})) \cdot (6 \sqrt{3})$

Step 1.3

Rewrite the expression.

$6 \sqrt{3} \cdot (6 \sqrt{3})$

Step 2

Multiply $6 \sqrt{3} (6 \sqrt{3})$ .

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Step 2.1

Multiply $6$ by $6$ .

$36 \sqrt{3} \sqrt{3}$

Step 2.2

Raise $\sqrt{3}$ to the power of $1$ .

$36 ({\sqrt{3}}^{1} \sqrt{3})$

Step 2.3

Raise $\sqrt{3}$ to the power of $1$ .

$36 ({\sqrt{3}}^{1} {\sqrt{3}}^{1})$

Step 2.4

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

$36 {\sqrt{3}}^{1 + 1}$

Step 2.5

Add $1$ and $1$ .

$36 {\sqrt{3}}^{2}$

Step 3

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

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Step 3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$36 {(3^{\frac{1}{2}})}^{2}$

Step 3.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$36 \cdot 3^{\frac{1}{2} \cdot 2}$

Step 3.3

Combine $\frac{1}{2}$ and $2$ .

$36 \cdot 3^{\frac{2}{2}}$

Step 3.4

Cancel the common factor of $2$ .

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Step 3.4.1

Cancel the common factor.

$36 \cdot 3^{\frac{2}{2}}$

Step 3.4.2

Rewrite the expression.

$36 \cdot 3^{1}$

Step 3.5

Evaluate the exponent.

$36 \cdot 3$

Step 4

Multiply $36$ by $3$ .

$108$