Basic Math Examples

$36000 = 5.67 \cdot 10^{- 8} \cdot 0.5026 \cdot t^{4}$

Step 1

Rewrite the equation as $5.67 \cdot 10^{- 8} \cdot 0.5026 \cdot t^{4} = 36000$ .

$5.67 \cdot 10^{- 8} \cdot 0.5026 \cdot t^{4} = 36000$

Step 2

Multiply $5.67$ by $0.5026$ .

$2.849742 \cdot 10^{- 8} \cdot t^{4} = 36000$

Step 3

Divide each term in $2.849742 \cdot 10^{- 8} \cdot t^{4} = 36000$ by $2.849742 \cdot 10^{- 8}$ and simplify.

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Step 3.1

Divide each term in $2.849742 \cdot 10^{- 8} \cdot t^{4} = 36000$ by $2.849742 \cdot 10^{- 8}$ .

$\frac{2.849742 \cdot 10^{- 8} \cdot t^{4}}{2.849742 \cdot 10^{- 8}} = \frac{36000}{2.849742 \cdot 10^{- 8}}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $2.849742$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{2.849742 \cdot 10^{- 8} \cdot t^{4}}{2.849742 \cdot 10^{- 8}} = \frac{36000}{2.849742 \cdot 10^{- 8}}$

Step 3.2.1.2

Rewrite the expression.

$\frac{10^{- 8} \cdot t^{4}}{10^{- 8}} = \frac{36000}{2.849742 \cdot 10^{- 8}}$

Step 3.2.2

Cancel the common factor of $10^{- 8}$ .

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Step 3.2.2.1

Cancel the common factor.

$\frac{10^{- 8} \cdot t^{4}}{10^{- 8}} = \frac{36000}{2.849742 \cdot 10^{- 8}}$

Step 3.2.2.2

Divide $t^{4}$ by $1$ .

$t^{4} = \frac{36000}{2.849742 \cdot 10^{- 8}}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide using scientific notation.

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Step 3.3.1.1

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

$t^{4} = (\frac{36000}{2.849742}) (\frac{1}{10^{- 8}})$

Step 3.3.1.2

Divide $36000$ by $2.849742$ .

$t^{4} = 12632.72254119 \frac{1}{10^{- 8}}$

Step 3.3.1.3

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

$t^{4} = 12632.72254119 \cdot 10^{8}$

Step 3.3.2

Move the decimal point in $12632.72254119$ to the left by $4$ places and increase the power of $10^{8}$ by $4$ .

$t^{4} = 1.26327225 \cdot 10^{12}$

Step 4

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$t = \pm \sqrt[4]{1.26327225 \cdot 10^{12}}$

Step 5

Simplify $\pm \sqrt[4]{1.26327225 \cdot 10^{12}}$ .

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Step 5.1

Rewrite $\sqrt[4]{1.26327225 \cdot 10^{12}}$ as $\sqrt[4]{1.26327225} \cdot \sqrt[4]{10^{12}}$ .

$t = \pm \sqrt[4]{1.26327225} \cdot \sqrt[4]{10^{12}}$

Step 5.2

Evaluate the root.

$t = \pm 1.06016689 \cdot \sqrt[4]{10^{12}}$

Step 5.3

Rewrite $10^{12}$ as ${(10^{3})}^{4}$ .

$t = \pm 1.06016689 \cdot \sqrt[4]{{(10^{3})}^{4}}$

Step 5.4

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

$t = \pm 1.06016689 \cdot 10^{3}$

Step 6

The complete solution is the result of both the positive and negative portions of the solution.

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Step 6.1

First, use the positive value of the $\pm$ to find the first solution.

$t = 1.06016689 \cdot 10^{3}$

Step 6.2

Next, use the negative value of the $\pm$ to find the second solution.

$t = - 1.06016689 \cdot 10^{3}$

Step 6.3

The complete solution is the result of both the positive and negative portions of the solution.

$t = 1.06016689 \cdot 10^{3}, - 1.06016689 \cdot 10^{3}$

Step 7

The result can be shown in multiple forms.

Scientific Notation:

$t = 1.06016689 \cdot 10^{3}, - 1.06016689 \cdot 10^{3}$

Expanded Form:

$t = 1060.16689664, - 1060.16689664$