Basic Math Examples

${(\frac{5}{4} (424333 - 10220^{2}))}^{\frac{1}{2}}$

Step 1

Simplify each term.

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Step 1.1

Raise

$10220$ to the power of

$2$ .

${(\frac{5}{4} \cdot (424333 - 1 \cdot 104448400))}^{\frac{1}{2}}$

Step 1.2

Multiply

$- 1$ by

$104448400$ .

${(\frac{5}{4} \cdot (424333 - 104448400))}^{\frac{1}{2}}$

Step 2

Subtract

$104448400$ from

$424333$ .

${(\frac{5}{4} \cdot - 104024067)}^{\frac{1}{2}}$

Step 3

Multiply

$\frac{5}{4} \cdot - 104024067$ .

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Step 3.1

Combine

$\frac{5}{4}$ and

$- 104024067$ .

${(\frac{5 \cdot - 104024067}{4})}^{\frac{1}{2}}$

Step 3.2

Multiply

$5$ by

$- 104024067$ .

${(\frac{- 520120335}{4})}^{\frac{1}{2}}$

Step 4

Move the negative in front of the fraction.

${(- \frac{520120335}{4})}^{\frac{1}{2}}$

Step 5

Use the power rule

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

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Step 5.1

Apply the product rule to

$- \frac{520120335}{4}$ .

${(- 1)}^{\frac{1}{2}} {(\frac{520120335}{4})}^{\frac{1}{2}}$

Step 5.2

Apply the product rule to

$\frac{520120335}{4}$ .

${(- 1)}^{\frac{1}{2}} \frac{520120335^{\frac{1}{2}}}{4^{\frac{1}{2}}}$

Step 6

Rewrite

${(- 1)}^{\frac{1}{2}}$ as

$\sqrt{{(- 1)}^{1}}$ .

$\sqrt{{(- 1)}^{1}} \frac{520120335^{\frac{1}{2}}}{4^{\frac{1}{2}}}$

Step 7

Evaluate the exponent.

$\sqrt{- 1} \frac{520120335^{\frac{1}{2}}}{4^{\frac{1}{2}}}$

Step 8

Rewrite

$\sqrt{- 1}$ as

$i$ .

$i \frac{520120335^{\frac{1}{2}}}{4^{\frac{1}{2}}}$

Step 9

Simplify the denominator.

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Step 9.1

Rewrite

$4$ as

$2^{2}$ .

$i \frac{520120335^{\frac{1}{2}}}{{(2^{2})}^{\frac{1}{2}}}$

Step 9.2

Apply the power rule and multiply exponents,

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

$i \frac{520120335^{\frac{1}{2}}}{2^{2 (\frac{1}{2})}}$

Step 9.3

Cancel the common factor of

$2$ .

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Step 9.3.1

Cancel the common factor.

$i \frac{520120335^{\frac{1}{2}}}{2^{2 (\frac{1}{2})}}$

Step 9.3.2

Rewrite the expression.

$i \frac{520120335^{\frac{1}{2}}}{2^{1}}$

Step 9.4

Evaluate the exponent.

$i \frac{520120335^{\frac{1}{2}}}{2}$

Step 10

Combine

$i$ and

$\frac{520120335^{\frac{1}{2}}}{2}$ .

$\frac{i \cdot 520120335^{\frac{1}{2}}}{2}$