Finite Math Examples

$(p \cdot \frac{{0.06985}^{3}}{32}) \cdot ({({(0.5 \cdot \frac{9656.4}{230000000})}^{2} + \frac{3}{4} \cdot {(\frac{2800}{270000000})}^{2})}^{- \frac{1}{2}})$

Step 1

Simplify the expression.

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Step 1.1

Raise $0.06985$ to the power of $3$ .

$p \cdot \frac{0.00034079}{32} \cdot {({(0.5 \cdot \frac{9656.4}{230000000})}^{2} + \frac{3}{4} \cdot {(\frac{2800}{270000000})}^{2})}^{- \frac{1}{2}}$

Step 1.2

Divide $0.00034079$ by $32$ .

$p \cdot 0.00001064 \cdot {({(0.5 \cdot \frac{9656.4}{230000000})}^{2} + \frac{3}{4} \cdot {(\frac{2800}{270000000})}^{2})}^{- \frac{1}{2}}$

Step 1.3

Move $0.00001064$ to the left of $p$ .

$0.00001064 \cdot p \cdot {({(0.5 \cdot \frac{9656.4}{230000000})}^{2} + \frac{3}{4} \cdot {(\frac{2800}{270000000})}^{2})}^{- \frac{1}{2}}$

Step 2

Simplify each term.

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Step 2.1

Cancel the common factor of $0.5$ .

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Step 2.1.1

Factor $0.5$ out of $230000000$ .

$0.00001064 p \cdot {({(0.5 \cdot \frac{9656.4}{0.5 (460000000)})}^{2} + \frac{3}{4} \cdot {(\frac{2800}{270000000})}^{2})}^{- \frac{1}{2}}$

Step 2.1.2

Cancel the common factor.

$0.00001064 p \cdot {({(0.5 \cdot \frac{9656.4}{0.5 \cdot 460000000})}^{2} + \frac{3}{4} \cdot {(\frac{2800}{270000000})}^{2})}^{- \frac{1}{2}}$

Step 2.1.3

Rewrite the expression.

$0.00001064 p \cdot {({(\frac{9656.4}{460000000})}^{2} + \frac{3}{4} \cdot {(\frac{2800}{270000000})}^{2})}^{- \frac{1}{2}}$

Step 2.2

Divide $9656.4$ by $460000000$ .

$0.00001064 p \cdot {({0.00002099}^{2} + \frac{3}{4} \cdot {(\frac{2800}{270000000})}^{2})}^{- \frac{1}{2}}$

Step 2.3

Raise $0.00002099$ to the power of $2$ .

$0.00001064 p \cdot {(0 + \frac{3}{4} \cdot {(\frac{2800}{270000000})}^{2})}^{- \frac{1}{2}}$

Step 2.4

Cancel the common factor of $2800$ and $270000000$ .

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Step 2.4.1

Factor $400$ out of $2800$ .

$0.00001064 p \cdot {(0 + \frac{3}{4} \cdot {(\frac{400 (7)}{270000000})}^{2})}^{- \frac{1}{2}}$

Step 2.4.2

Cancel the common factors.

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Step 2.4.2.1

Factor $400$ out of $270000000$ .

$0.00001064 p \cdot {(0 + \frac{3}{4} \cdot {(\frac{400 \cdot 7}{400 \cdot 675000})}^{2})}^{- \frac{1}{2}}$

Step 2.4.2.2

Cancel the common factor.

$0.00001064 p \cdot {(0 + \frac{3}{4} \cdot {(\frac{400 \cdot 7}{400 \cdot 675000})}^{2})}^{- \frac{1}{2}}$

Step 2.4.2.3

Rewrite the expression.

$0.00001064 p \cdot {(0 + \frac{3}{4} \cdot {(\frac{7}{675000})}^{2})}^{- \frac{1}{2}}$

Step 2.5

Apply the product rule to $\frac{7}{675000}$ .

$0.00001064 p \cdot {(0 + \frac{3}{4} \cdot \frac{7^{2}}{675000^{2}})}^{- \frac{1}{2}}$

Step 2.6

Combine.

$0.00001064 p \cdot {(0 + \frac{3 \cdot 7^{2}}{4 \cdot 675000^{2}})}^{- \frac{1}{2}}$

Step 2.7

Raise $7$ to the power of $2$ .

$0.00001064 p \cdot {(0 + \frac{3 \cdot 49}{4 \cdot 675000^{2}})}^{- \frac{1}{2}}$

Step 2.8

Raise $675000$ to the power of $2$ .

$0.00001064 p \cdot {(0 + \frac{3 \cdot 49}{4 \cdot 455625000000})}^{- \frac{1}{2}}$

Step 2.9

Multiply $3$ by $49$ .

$0.00001064 p \cdot {(0 + \frac{147}{4 \cdot 455625000000})}^{- \frac{1}{2}}$

Step 2.10

Multiply $4$ by $455625000000$ .

$0.00001064 p \cdot {(0 + \frac{147}{1822500000000})}^{- \frac{1}{2}}$

Step 2.11

Cancel the common factor of $147$ and $1822500000000$ .

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Step 2.11.1

Factor $3$ out of $147$ .

$0.00001064 p \cdot {(0 + \frac{3 (49)}{1822500000000})}^{- \frac{1}{2}}$

Step 2.11.2

Cancel the common factors.

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Step 2.11.2.1

Factor $3$ out of $1822500000000$ .

$0.00001064 p \cdot {(0 + \frac{3 \cdot 49}{3 \cdot 607500000000})}^{- \frac{1}{2}}$

Step 2.11.2.2

Cancel the common factor.

$0.00001064 p \cdot {(0 + \frac{3 \cdot 49}{3 \cdot 607500000000})}^{- \frac{1}{2}}$

Step 2.11.2.3

Rewrite the expression.

$0.00001064 p \cdot {(0 + \frac{49}{607500000000})}^{- \frac{1}{2}}$

Step 3

Add $0$ and $\frac{49}{607500000000}$ .

$0.00001064 p \cdot 0^{- \frac{1}{2}}$

Step 4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$0.00001064 p \cdot \frac{1}{0^{\frac{1}{2}}}$

Step 5

Simplify the denominator.

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Step 5.1

Rewrite $0$ as ${0.00002283}^{2}$ .

$0.00001064 p \cdot \frac{1}{{({0.00002283}^{2})}^{\frac{1}{2}}}$

Step 5.2

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

$0.00001064 p \cdot \frac{1}{{0.00002283}^{2 (\frac{1}{2})}}$

Step 5.3

Cancel the common factor of $2$ .

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Step 5.3.1

Cancel the common factor.

$0.00001064 p \cdot \frac{1}{{0.00002283}^{2 (\frac{1}{2})}}$

Step 5.3.2

Rewrite the expression.

$0.00001064 p \cdot \frac{1}{{0.00002283}^{1}}$

Step 5.4

Evaluate the exponent.

$0.00001064 p \cdot \frac{1}{0.00002283}$

Step 6

Simplify the expression.

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Step 6.1

Divide $1$ by $0.00002283$ .

$0.00001064 p \cdot 43796.9355265$

Step 6.2

Multiply $43796.9355265$ by $0.00001064$ .

$0.46643698 p$