Basic Math Examples

$100 + 50 \cdot \sqrt[10]{1} \div \sqrt[6]{64} - 505 \div 4^{\frac{1}{2}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite the division as a fraction.

$100 + \frac{50 \cdot \sqrt[10]{1}}{\sqrt[6]{64}} - 505 \div 4^{\frac{1}{2}}$

Step 1.2

Any root of $1$ is $1$ .

$100 + \frac{50 \cdot 1}{\sqrt[6]{64}} - 505 \div 4^{\frac{1}{2}}$

Step 1.3

Simplify the denominator.

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Step 1.3.1

Rewrite $64$ as $2^{6}$ .

$100 + \frac{50 \cdot 1}{\sqrt[6]{2^{6}}} - 505 \div 4^{\frac{1}{2}}$

Step 1.3.2

Pull terms out from under the radical, assuming positive real numbers.

$100 + \frac{50 \cdot 1}{2} - 505 \div 4^{\frac{1}{2}}$

Step 1.4

Multiply $50$ by $1$ .

$100 + \frac{50}{2} - 505 \div 4^{\frac{1}{2}}$

Step 1.5

Divide $50$ by $2$ .

$100 + 25 - 505 \div 4^{\frac{1}{2}}$

Step 1.6

Rewrite the division as a fraction.

$100 + 25 - \frac{505}{4^{\frac{1}{2}}}$

Step 1.7

Simplify the denominator.

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Step 1.7.1

Rewrite $4$ as $2^{2}$ .

$100 + 25 - \frac{505}{{(2^{2})}^{\frac{1}{2}}}$

Step 1.7.2

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

$100 + 25 - \frac{505}{2^{2 (\frac{1}{2})}}$

Step 1.7.3

Cancel the common factor of $2$ .

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Step 1.7.3.1

Cancel the common factor.

$100 + 25 - \frac{505}{2^{2 (\frac{1}{2})}}$

Step 1.7.3.2

Rewrite the expression.

$100 + 25 - \frac{505}{2^{1}}$

Step 1.7.4

Evaluate the exponent.

$100 + 25 - \frac{505}{2}$

Step 2

Find the common denominator.

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Step 2.1

Write $100$ as a fraction with denominator $1$ .

$\frac{100}{1} + 25 - \frac{505}{2}$

Step 2.2

Multiply $\frac{100}{1}$ by $\frac{2}{2}$ .

$\frac{100}{1} \cdot \frac{2}{2} + 25 - \frac{505}{2}$

Step 2.3

Multiply $\frac{100}{1}$ by $\frac{2}{2}$ .

$\frac{100 \cdot 2}{2} + 25 - \frac{505}{2}$

Step 2.4

Write $25$ as a fraction with denominator $1$ .

$\frac{100 \cdot 2}{2} + \frac{25}{1} - \frac{505}{2}$

Step 2.5

Multiply $\frac{25}{1}$ by $\frac{2}{2}$ .

$\frac{100 \cdot 2}{2} + \frac{25}{1} \cdot \frac{2}{2} - \frac{505}{2}$

Step 2.6

Multiply $\frac{25}{1}$ by $\frac{2}{2}$ .

$\frac{100 \cdot 2}{2} + \frac{25 \cdot 2}{2} - \frac{505}{2}$

Step 3

Combine the numerators over the common denominator.

$\frac{100 \cdot 2 + 25 \cdot 2 - 505}{2}$

Step 4

Simplify each term.

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Step 4.1

Multiply $100$ by $2$ .

$\frac{200 + 25 \cdot 2 - 505}{2}$

Step 4.2

Multiply $25$ by $2$ .

$\frac{200 + 50 - 505}{2}$

Step 5

Simplify the expression.

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Step 5.1

Add $200$ and $50$ .

$\frac{250 - 505}{2}$

Step 5.2

Subtract $505$ from $250$ .

$\frac{- 255}{2}$

Step 5.3

Move the negative in front of the fraction.

$- \frac{255}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{255}{2}$

Decimal Form:

$- 127.5$

Mixed Number Form:

$- 127 \frac{1}{2}$