Finite Math Examples

$10000 {(\frac{92}{100})}^{3} {(\frac{90}{100})}^{7}$

Step 1

Cancel the common factor of $92$ and $100$ .

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Step 1.1

Factor $4$ out of $92$ .

$10000 {(\frac{4 (23)}{100})}^{3} {(\frac{90}{100})}^{7}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $4$ out of $100$ .

$10000 {(\frac{4 \cdot 23}{4 \cdot 25})}^{3} {(\frac{90}{100})}^{7}$

Step 1.2.2

Cancel the common factor.

$10000 {(\frac{4 \cdot 23}{4 \cdot 25})}^{3} {(\frac{90}{100})}^{7}$

Step 1.2.3

Rewrite the expression.

$10000 {(\frac{23}{25})}^{3} {(\frac{90}{100})}^{7}$

Step 2

Simplify the expression.

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Step 2.1

Apply the product rule to $\frac{23}{25}$ .

$10000 \frac{23^{3}}{25^{3}} {(\frac{90}{100})}^{7}$

Step 2.2

Raise $23$ to the power of $3$ .

$10000 \frac{12167}{25^{3}} {(\frac{90}{100})}^{7}$

Step 2.3

Raise $25$ to the power of $3$ .

$10000 (\frac{12167}{15625}) {(\frac{90}{100})}^{7}$

Step 3

Cancel the common factor of $625$ .

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Step 3.1

Factor $625$ out of $10000$ .

$625 (16) \frac{12167}{15625} {(\frac{90}{100})}^{7}$

Step 3.2

Factor $625$ out of $15625$ .

$625 \cdot 16 \frac{12167}{625 \cdot 25} {(\frac{90}{100})}^{7}$

Step 3.3

Cancel the common factor.

$625 \cdot 16 \frac{12167}{625 \cdot 25} {(\frac{90}{100})}^{7}$

Step 3.4

Rewrite the expression.

$16 (\frac{12167}{25}) {(\frac{90}{100})}^{7}$

Step 4

Combine $16$ and $\frac{12167}{25}$ .

$\frac{16 \cdot 12167}{25} {(\frac{90}{100})}^{7}$

Step 5

Multiply $16$ by $12167$ .

$\frac{194672}{25} {(\frac{90}{100})}^{7}$

Step 6

Cancel the common factor of $90$ and $100$ .

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Step 6.1

Factor $10$ out of $90$ .

$\frac{194672}{25} {(\frac{10 (9)}{100})}^{7}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $10$ out of $100$ .

$\frac{194672}{25} {(\frac{10 \cdot 9}{10 \cdot 10})}^{7}$

Step 6.2.2

Cancel the common factor.

$\frac{194672}{25} {(\frac{10 \cdot 9}{10 \cdot 10})}^{7}$

Step 6.2.3

Rewrite the expression.

$\frac{194672}{25} {(\frac{9}{10})}^{7}$

Step 7

Apply the product rule to $\frac{9}{10}$ .

$\frac{194672}{25} \cdot \frac{9^{7}}{10^{7}}$

Step 8

Combine.

$\frac{194672 \cdot 9^{7}}{25 \cdot 10^{7}}$

Step 9

Simplify the expression.

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Step 9.1

Raise $9$ to the power of $7$ .

$\frac{194672 \cdot 4782969}{25 \cdot 10^{7}}$

Step 9.2

Multiply $194672$ by $4782969$ .

$\frac{931110141168}{25 \cdot 10^{7}}$

Step 10

Divide using scientific notation.

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Step 10.1

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

$(\frac{931110141168}{25}) (\frac{1}{10^{7}})$

Step 10.2

Divide $931110141168$ by $25$ .

$37244405646.72 \frac{1}{10^{7}}$

Step 10.3

Move $10^{7}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$37244405646.72 \cdot 10^{- 7}$

Step 11

Move the decimal point in $37244405646.72$ to the left by $10$ places and increase the power of $10^{- 7}$ by $10$ .

$3.72444056 \cdot 10^{3}$

Step 12

The result can be shown in multiple forms.

Scientific Notation:

$3.72444056 \cdot 10^{3}$

Expanded Form:

$3724.44056467$