Algebra Examples

${(2 \cdot \sqrt{6})}^{4}$

Step 1

Simplify the expression.

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Step 1.1

Apply the product rule to $2 \sqrt{6}$ .

$2^{4} {\sqrt{6}}^{4}$

Step 1.2

Raise $2$ to the power of $4$ .

$16 {\sqrt{6}}^{4}$

Step 2

Rewrite ${\sqrt{6}}^{4}$ as $6^{2}$ .

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Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6}$ as $6^{\frac{1}{2}}$ .

$16 {(6^{\frac{1}{2}})}^{4}$

Step 2.2

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

$16 \cdot 6^{\frac{1}{2} \cdot 4}$

Step 2.3

Combine $\frac{1}{2}$ and $4$ .

$16 \cdot 6^{\frac{4}{2}}$

Step 2.4

Cancel the common factor of $4$ and $2$ .

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Step 2.4.1

Factor $2$ out of $4$ .

$16 \cdot 6^{\frac{2 \cdot 2}{2}}$

Step 2.4.2

Cancel the common factors.

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Step 2.4.2.1

Factor $2$ out of $2$ .

$16 \cdot 6^{\frac{2 \cdot 2}{2 (1)}}$

Step 2.4.2.2

Cancel the common factor.

$16 \cdot 6^{\frac{2 \cdot 2}{2 \cdot 1}}$

Step 2.4.2.3

Rewrite the expression.

$16 \cdot 6^{\frac{2}{1}}$

Step 2.4.2.4

Divide $2$ by $1$ .

$16 \cdot 6^{2}$

Step 3

Simplify the expression.

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Step 3.1

Raise $6$ to the power of $2$ .

$16 \cdot 36$

Step 3.2

Multiply $16$ by $36$ .

$576$