Algebra Examples

${(\sqrt{6} (c i s^{120}))}^{4}$

Step 1

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

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Step 1.1

Apply the product rule to $\sqrt{6} c i s^{120}$ .

${(\sqrt{6} c i)}^{4} {(s^{120})}^{4}$

Step 1.2

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

${(\sqrt{6} c)}^{4} i^{4} {(s^{120})}^{4}$

Step 1.3

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

${\sqrt{6}}^{4} c^{4} i^{4} {(s^{120})}^{4}$

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 $6^{\frac{1}{2}}$ .

${(6^{\frac{1}{2}})}^{4} c^{4} i^{4} {(s^{120})}^{4}$

Step 2.2

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

$6^{\frac{1}{2} \cdot 4} c^{4} i^{4} {(s^{120})}^{4}$

Step 2.3

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

$6^{\frac{4}{2}} c^{4} i^{4} {(s^{120})}^{4}$

Step 2.4

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

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Step 2.4.1

Factor $2$ out of $4$ .

$6^{\frac{2 \cdot 2}{2}} c^{4} i^{4} {(s^{120})}^{4}$

Step 2.4.2

Cancel the common factors.

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Step 2.4.2.1

Factor $2$ out of $2$ .

$6^{\frac{2 \cdot 2}{2 (1)}} c^{4} i^{4} {(s^{120})}^{4}$

Step 2.4.2.2

Cancel the common factor.

$6^{\frac{2 \cdot 2}{2 \cdot 1}} c^{4} i^{4} {(s^{120})}^{4}$

Step 2.4.2.3

Rewrite the expression.

$6^{\frac{2}{1}} c^{4} i^{4} {(s^{120})}^{4}$

Step 2.4.2.4

Divide $2$ by $1$ .

$6^{2} c^{4} i^{4} {(s^{120})}^{4}$

Step 3

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

$36 c^{4} i^{4} {(s^{120})}^{4}$

Step 4

Rewrite $i^{4}$ as $1$ .

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Step 4.1

Rewrite $i^{4}$ as ${(i^{2})}^{2}$ .

$36 c^{4} {(i^{2})}^{2} {(s^{120})}^{4}$

Step 4.2

Rewrite $i^{2}$ as $- 1$ .

$36 c^{4} {(- 1)}^{2} {(s^{120})}^{4}$

Step 4.3

Raise $- 1$ to the power of $2$ .

$36 c^{4} \cdot 1 {(s^{120})}^{4}$

Step 5

Multiply $36$ by $1$ .

$36 c^{4} {(s^{120})}^{4}$

Step 6

Multiply the exponents in ${(s^{120})}^{4}$ .

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Step 6.1

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

$36 c^{4} s^{120 \cdot 4}$

Step 6.2

Multiply $120$ by $4$ .

$36 c^{4} s^{480}$