Basic Math Examples

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

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

Step 1

Use the power rule

{(a b)}^{n} = a^{n} b^{n}

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

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Step 1.1

Apply the product rule to

2 R \sqrt{2}

$2 R \sqrt{2}$ .

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

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

Step 1.2

Apply the product rule to

2 R

$2 R$ .

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

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

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

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

Step 2

Raise

2

$2$ to the power of

2

$2$ .

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

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

Step 3

Rewrite

{\sqrt{2}}^{2}

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

2

$2$ .

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Step 3.1

Use

\sqrt[n]{a^{x}} = a^{\frac{x}{n}}

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

\sqrt{2}

$\sqrt{2}$ as

2^{\frac{1}{2}}

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

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

${(a^{m})}^{n} = a^{m n}$ .

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

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

Step 3.3

Combine

\frac{1}{2}

$\frac{1}{2}$ and

2

$2$ .

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

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

Step 3.4

Cancel the common factor of

2

$2$ .

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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.

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

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

Step 3.5

Evaluate the exponent.

$4 R^{2} \cdot 2$

$4 R^{2} \cdot 2$

Step 4

Multiply

$2$ by

$4$ .

$8 R^{2}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$