Finite Math Examples

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

Step 1

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

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

Step 2

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

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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.

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

Step 2.1.2

Divide $1366$ by $5.67$ .

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

Step 2.1.3

Move $10^{- 8}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 2.2

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

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

Step 2.3

Evaluate the root.

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

Step 2.4

Rewrite $10^{8}$ as ${(10^{2})}^{4}$ .

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

Step 2.5

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

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

Step 2.6

Simplify the expression.

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Step 2.6.1

Convert $0.3 %$ to a decimal.

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

Step 2.6.2

Multiply $- 1$ by $0.003$ .

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

Step 2.6.3

Subtract $0.003$ from $1$ .

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

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:

$t = 393.67759571$