Finite Math Examples

t = \sqrt[4]{\frac{1366}{5.67 \cdot 10^{- 8}}} (\sqrt[4]{1 - 0.3 %})

$t = \sqrt[4]{\frac{1366}{5.67 \cdot 10^{- 8}}} (\sqrt[4]{1 - 0.3 %})$

Step 1

Multiply

\sqrt[4]{\frac{1366}{5.67 \cdot 10^{- 8}}}

$\sqrt[4]{\frac{1366}{5.67 \cdot 10^{- 8}}}$ by

\sqrt[4]{1 - 0.3 %}

$\sqrt[4]{1 - 0.3 %}$ .

t = \sqrt[4]{\frac{1366}{5.67 \cdot 10^{- 8}}} \sqrt[4]{1 - 0.3 %}

$t = \sqrt[4]{\frac{1366}{5.67 \cdot 10^{- 8}}} \sqrt[4]{1 - 0.3 %}$

Step 2

Simplify

\sqrt[4]{\frac{1366}{5.67 \cdot 10^{- 8}}} \sqrt[4]{1 - 0.3 %}

$\sqrt[4]{\frac{1366}{5.67 \cdot 10^{- 8}}} \sqrt[4]{1 - 0.3 %}$ .

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Step 2.1

Divide using scientific notation.

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Step 2.1.1

Group coefficients together and exponents together to divide numbers in scientific notation.

t = \sqrt[4]{(\frac{1366}{5.67}) (\frac{1}{10^{- 8}})} \sqrt[4]{1 - 0.3 %}

$t = \sqrt[4]{(\frac{1366}{5.67}) (\frac{1}{10^{- 8}})} \sqrt[4]{1 - 0.3 %}$

Step 2.1.2

Divide

1366

$1366$ by

5.67

$5.67$ .

t = \sqrt[4]{240.91710758 \frac{1}{10^{- 8}}} \sqrt[4]{1 - 0.3 %}

$t = \sqrt[4]{240.91710758 \frac{1}{10^{- 8}}} \sqrt[4]{1 - 0.3 %}$

Step 2.1.3

Move

10^{- 8}

$10^{- 8}$ to the numerator using the negative exponent rule

\frac{1}{b^{- n}} = b^{n}

$\frac{1}{b^{- n}} = b^{n}$ .

t = \sqrt[4]{240.91710758 \cdot 10^{8}} \sqrt[4]{1 - 0.3 %}

$t = \sqrt[4]{240.91710758 \cdot 10^{8}} \sqrt[4]{1 - 0.3 %}$

t = \sqrt[4]{240.91710758 \cdot 10^{8}} \sqrt[4]{1 - 0.3 %}

$t = \sqrt[4]{240.91710758 \cdot 10^{8}} \sqrt[4]{1 - 0.3 %}$

Step 2.2

Rewrite

\sqrt[4]{240.91710758 \cdot 10^{8}}

$\sqrt[4]{240.91710758 \cdot 10^{8}}$ as

\sqrt[4]{240.91710758} \cdot \sqrt[4]{10^{8}}

$\sqrt[4]{240.91710758} \cdot \sqrt[4]{10^{8}}$ .

t = \sqrt[4]{240.91710758} \cdot \sqrt[4]{10^{8}} \sqrt[4]{1 - 0.3 %}

$t = \sqrt[4]{240.91710758} \cdot \sqrt[4]{10^{8}} \sqrt[4]{1 - 0.3 %}$

Step 2.3

Evaluate the root.

t = 3.93973408 \cdot \sqrt[4]{10^{8}} \sqrt[4]{1 - 0.3 %}

$t = 3.93973408 \cdot \sqrt[4]{10^{8}} \sqrt[4]{1 - 0.3 %}$

Step 2.4

Rewrite

10^{8}

$10^{8}$ as

{(10^{2})}^{4}

${(10^{2})}^{4}$ .

t = 3.93973408 \cdot \sqrt[4]{{(10^{2})}^{4}} \sqrt[4]{1 - 0.3 %}

$t = 3.93973408 \cdot \sqrt[4]{{(10^{2})}^{4}} \sqrt[4]{1 - 0.3 %}$

Step 2.5

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

t = 3.93973408 \cdot 10^{2} \sqrt[4]{1 - 0.3 %}

$t = 3.93973408 \cdot 10^{2} \sqrt[4]{1 - 0.3 %}$

Step 2.6

Simplify the expression.

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Step 2.6.1

Convert

0.3 %

$0.3 %$ to a decimal.

t = 3.93973408 \cdot 10^{2} \sqrt[4]{1 - 1 \cdot 0.003}

$t = 3.93973408 \cdot 10^{2} \sqrt[4]{1 - 1 \cdot 0.003}$

Step 2.6.2

Multiply

- 1

$- 1$ by

0.003

$0.003$ .

t = 3.93973408 \cdot 10^{2} \sqrt[4]{1 - 0.003}

$t = 3.93973408 \cdot 10^{2} \sqrt[4]{1 - 0.003}$

Step 2.6.3

Subtract

0.003

$0.003$ from

1

$1$ .

t = 3.93973408 \cdot 10^{2} \sqrt[4]{0.997}

$t = 3.93973408 \cdot 10^{2} \sqrt[4]{0.997}$

Step 2.7

Multiply

$\sqrt[4]{0.997}$ by

$3.93973408$ .

$t = 3.93677595 \cdot 10^{2}$

Step 3

The result can be shown in multiple forms.

Scientific Notation:

$t = 3.93677595 \cdot 10^{2}$

Expanded Form:

$t = 393.67759571$