Basic Math Examples

${(2 R \sqrt{2})}^{2}$

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 $2 R \sqrt{2}$ .

${(2 R)}^{2} {\sqrt{2}}^{2}$

Step 1.2

Apply the product rule to $2 R$ .

$2^{2} R^{2} {\sqrt{2}}^{2}$

Step 2

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

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

Step 3

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

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Step 3.1

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

$4 R^{2} {(2^{\frac{1}{2}})}^{2}$

Step 3.2

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

$4 R^{2} \cdot 2^{\frac{1}{2} \cdot 2}$

Step 3.3

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

$4 R^{2} \cdot 2^{\frac{2}{2}}$

Step 3.4

Cancel the common factor of $2$ .

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Step 3.4.1

Cancel the common factor.

$4 R^{2} \cdot 2^{\frac{2}{2}}$

Step 3.4.2

Rewrite the expression.

$4 R^{2} \cdot 2^{1}$

Step 3.5

Evaluate the exponent.

$4 R^{2} \cdot 2$

Step 4

Multiply $2$ by $4$ .

$8 R^{2}$