Calculus Examples

$\sqrt{11 c} \cdot \sqrt{11 c}$

Step 1

Multiply $\sqrt{11 c} \sqrt{11 c}$ .

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Step 1.1

Raise $\sqrt{11 c}$ to the power of $1$ .

${\sqrt{11 c}}^{1} \sqrt{11 c}$

Step 1.2

Raise $\sqrt{11 c}$ to the power of $1$ .

${\sqrt{11 c}}^{1} {\sqrt{11 c}}^{1}$

Step 1.3

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

${\sqrt{11 c}}^{1 + 1}$

Step 1.4

Add $1$ and $1$ .

${\sqrt{11 c}}^{2}$

Step 2

Rewrite ${\sqrt{11 c}}^{2}$ as $11 c$ .

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Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{11 c}$ as ${(11 c)}^{\frac{1}{2}}$ .

${({(11 c)}^{\frac{1}{2}})}^{2}$

Step 2.2

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

${(11 c)}^{\frac{1}{2} \cdot 2}$

Step 2.3

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

${(11 c)}^{\frac{2}{2}}$

Step 2.4

Cancel the common factor of $2$ .

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Step 2.4.1

Cancel the common factor.

${(11 c)}^{\frac{2}{2}}$

Step 2.4.2

Rewrite the expression.

${(11 c)}^{1}$

Step 2.5

Simplify.

$11 c$