Calculus Examples

$\frac{- p (- 3000 p^{- 4})}{\frac{1000}{p^{3}}}$

Step 1

Multiply $p$ by $p^{- 4}$ by adding the exponents.

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Step 1.1

Move $p^{- 4}$ .

$\frac{- (p^{- 4} p) \cdot - 3000}{\frac{1000}{p^{3}}}$

Step 1.2

Multiply $p^{- 4}$ by $p$ .

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Step 1.2.1

Raise $p$ to the power of $1$ .

$\frac{- (p^{- 4} p^{1}) \cdot - 3000}{\frac{1000}{p^{3}}}$

Step 1.2.2

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

$\frac{- p^{- 4 + 1} \cdot - 3000}{\frac{1000}{p^{3}}}$

Step 1.3

Add $- 4$ and $1$ .

$\frac{- p^{- 3} \cdot - 3000}{\frac{1000}{p^{3}}}$

Step 2

Move $p^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{- 1 \cdot - 3000}{\frac{1000}{p^{3}} p^{3}}$

Step 3

Combine $\frac{1000}{p^{3}}$ and $p^{3}$ .

$\frac{- 1 \cdot - 3000}{\frac{1000 p^{3}}{p^{3}}}$

Step 4

Cancel the common factor of $p^{3}$ .

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Step 4.1

Cancel the common factor.

$\frac{- 1 \cdot - 3000}{\frac{1000 p^{3}}{p^{3}}}$

Step 4.2

Divide $1000$ by $1$ .

$\frac{- 1 \cdot - 3000}{1000}$

Step 5

Cancel the common factor of $- 3000$ and $1000$ .

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Step 5.1

Factor $1000$ out of $- 1 \cdot - 3000$ .

$\frac{1000 (- 1 \cdot - 3)}{1000}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $1000$ out of $1000$ .

$\frac{1000 (- 1 \cdot - 3)}{1000 (1)}$

Step 5.2.2

Cancel the common factor.

$\frac{1000 (- 1 \cdot - 3)}{1000 \cdot 1}$

Step 5.2.3

Rewrite the expression.

$\frac{- 1 \cdot - 3}{1}$

Step 5.2.4

Divide $- 1 \cdot - 3$ by $1$ .

$- 1 \cdot - 3$

Step 6

Simplify the expression.

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Step 6.1

Rewrite $- 1 \cdot - 3$ as $- - 3$ .

$- - 3$

Step 6.2

Multiply $- 1$ by $- 3$ .

$3$