Calculus Examples

$t = (\frac{1.166 \cdot 10^{- 5}}{(6.582 \cdot 10^{- 25}) \cdot 16 \cdot p}) \cdot {| 0.9396 - 0.9425 |}^{6.905}$

Step 1

Multiply $6.582 \cdot 10^{- 25}$ by $16$ .

$t = \frac{1.166 \cdot 10^{- 5}}{6.582 \cdot 10^{- 25} \cdot 16 \cdot p} \cdot {| 0.9396 - 0.9425 |}^{6.905}$

Step 2

Simplify $\frac{1.166 \cdot 10^{- 5}}{6.582 \cdot 10^{- 25} \cdot 16 \cdot p} \cdot {| 0.9396 - 0.9425 |}^{6.905}$ .

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Step 2.1

Multiply $6.582$ by $16$ .

$t = \frac{1.166 \cdot 10^{- 5}}{105.312 \cdot 10^{- 25} \cdot p} \cdot {| 0.9396 - 0.9425 |}^{6.905}$

Step 2.2

Move $10^{- 25}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$t = \frac{1.166 \cdot 10^{- 5} \cdot 10^{25}}{105.312 \cdot p} \cdot {| 0.9396 - 0.9425 |}^{6.905}$

Step 2.3

Multiply $10^{- 5}$ by $10^{25}$ by adding the exponents.

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Step 2.3.1

Move $10^{25}$ .

$t = \frac{1.166 \cdot (10^{25} \cdot 10^{- 5})}{105.312 \cdot p} \cdot {| 0.9396 - 0.9425 |}^{6.905}$

Step 2.3.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$t = \frac{1.166 \cdot 10^{25 - 5}}{105.312 \cdot p} \cdot {| 0.9396 - 0.9425 |}^{6.905}$

Step 2.3.3

Subtract $5$ from $25$ .

$t = \frac{1.166 \cdot 10^{20}}{105.312 \cdot p} \cdot {| 0.9396 - 0.9425 |}^{6.905}$

Step 2.4

Multiply by $1$ .

$t = \frac{1 1.166 \cdot 10^{20}}{105.312 \cdot p} \cdot {| 0.9396 - 0.9425 |}^{6.905}$

Step 2.5

Factor $105.312$ out of $105.312 \cdot p$ .

$t = \frac{1 1.166 \cdot 10^{20}}{105.312 (p)} \cdot {| 0.9396 - 0.9425 |}^{6.905}$

Step 2.6

Separate fractions.

$t = \frac{1}{105.312} \cdot \frac{1.166 \cdot 10^{20}}{p} \cdot {| 0.9396 - 0.9425 |}^{6.905}$

Step 2.7

Divide $1$ by $105.312$ .

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Step 2.7.1

Move $10^{25}$ .

$t = 0.00949559 \frac{1.166 \cdot (10^{25} \cdot 10^{- 5})}{p} \cdot {| 0.9396 - 0.9425 |}^{6.905}$

Step 2.7.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$t = 0.00949559 \frac{1.166 \cdot 10^{25 - 5}}{p} \cdot {| 0.9396 - 0.9425 |}^{6.905}$

Step 2.7.3

Subtract $5$ from $25$ .

$t = 0.00949559 \frac{1.166 \cdot 10^{20}}{p} \cdot {| 0.9396 - 0.9425 |}^{6.905}$

Step 2.8

Multiply $0.00949559 \frac{1.166 \cdot 10^{20}}{p}$ .

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Step 2.8.1

Combine $0.00949559$ and $\frac{1.166 \cdot 10^{20}}{p}$ .

$t = \frac{0.00949559 \cdot 1.166 \cdot 10^{20}}{p} \cdot {| 0.9396 - 0.9425 |}^{6.905}$

Step 2.8.2

Multiply $1.166$ by $0.00949559$ .

$t = \frac{0.01107186 \cdot 10^{20}}{p} \cdot {| 0.9396 - 0.9425 |}^{6.905}$

Step 2.9

Move the decimal point in $0.01107186$ to the right by $2$ places and decrease the power of $10^{20}$ by $2$ .

$t = \frac{1.10718626 \cdot 10^{18}}{p} \cdot {| 0.9396 - 0.9425 |}^{6.905}$

Step 2.10

Subtract $0.9425$ from $0.9396$ .

$t = \frac{1.10718626 \cdot 10^{18}}{p} \cdot {| - 0.0029 |}^{6.905}$

Step 2.11

Remove non-negative terms from the absolute value.

$t = \frac{1.10718626 \cdot 10^{18}}{p} \cdot {0.0029}^{6.905}$

Step 2.12

Raise $0.0029$ to the power of $6.905$ .

$t = \frac{1.10718626 \cdot 10^{18}}{p} \cdot 0$

Step 2.13

Multiply $\frac{1.10718626 \cdot 10^{18}}{p} \cdot 0$ .

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Step 2.13.1

Combine $\frac{1.10718626 \cdot 10^{18}}{p}$ and $0$ .

$t = \frac{1.10718626 \cdot 10^{18} \cdot 0}{p}$

Step 2.13.2

Multiply $0$ by $1.10718626$ .

$t = \frac{0 \cdot 10^{18}}{p}$

Step 2.14

Simplify the numerator.

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Step 2.14.1

Move the decimal point in $0$ to the right by $18$ places and decrease the power of $10^{18}$ by $18$ .

$t = \frac{3.32719967 \cdot 10^{0}}{p}$

Step 2.14.2

Convert $3.32719967 \cdot 10^{0}$ from scientific notation.

$t = \frac{3.32719967}{p}$