Basic Math Examples

20^{2} = {(2 \cdot \sqrt{S})}^{2}

$20^{2} = {(2 \cdot \sqrt{S})}^{2}$

Step 1

Simplify

{(2 \cdot \sqrt{S})}^{2}

${(2 \cdot \sqrt{S})}^{2}$ .

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Step 1.1

Simplify the expression.

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Step 1.1.1

Apply the product rule to

2 \sqrt{S}

$2 \sqrt{S}$ .

20^{2} = 2^{2} {\sqrt{S}}^{2}

$20^{2} = 2^{2} {\sqrt{S}}^{2}$

Step 1.1.2

Raise

2

$2$ to the power of

2

$2$ .

20^{2} = 4 {\sqrt{S}}^{2}

$20^{2} = 4 {\sqrt{S}}^{2}$

20^{2} = 4 {\sqrt{S}}^{2}

$20^{2} = 4 {\sqrt{S}}^{2}$

Step 1.2

Rewrite

{\sqrt{S}}^{2}

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

S

$S$ .

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Step 1.2.1

Use

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

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

\sqrt{S}

$\sqrt{S}$ as

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

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

20^{2} = 4 {(S^{\frac{1}{2}})}^{2}

$20^{2} = 4 {(S^{\frac{1}{2}})}^{2}$

Step 1.2.2

Apply the power rule and multiply exponents,

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

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

20^{2} = 4 S^{\frac{1}{2} \cdot 2}

$20^{2} = 4 S^{\frac{1}{2} \cdot 2}$

Step 1.2.3

Combine

\frac{1}{2}

$\frac{1}{2}$ and

2

$2$ .

20^{2} = 4 S^{\frac{2}{2}}

$20^{2} = 4 S^{\frac{2}{2}}$

Step 1.2.4

Cancel the common factor of

2

$2$ .

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Step 1.2.4.1

Cancel the common factor.

$20^{2} = 4 S^{\frac{2}{2}}$

Step 1.2.4.2

Rewrite the expression.

$20^{2} = 4 S^{1}$

$20^{2} = 4 S^{1}$

Step 1.2.5

Simplify.

$20^{2} = 4 S$

$20^{2} = 4 S$

$20^{2} = 4 S$

Step 2

Rewrite the equation as

$4 S = 20^{2}$ .

$4 S = 20^{2}$

Step 3

Divide each term in

$4 S = 20^{2}$ by

$4$ and simplify.

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Step 3.1

Divide each term in

$4 S = 20^{2}$ by

$4$ .

$\frac{4 S}{4} = \frac{20^{2}}{4}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of

$4$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{4 S}{4} = \frac{20^{2}}{4}$

Step 3.2.1.2

Divide

$S$ by

$1$ .

$S = \frac{20^{2}}{4}$

$S = \frac{20^{2}}{4}$

$S = \frac{20^{2}}{4}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Raise

$20$ to the power of

$2$ .

$S = \frac{400}{4}$

Step 3.3.2

Divide

$400$ by

$4$ .

$S = 100$

$S = 100$

$S = 100$

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