Precalculus Examples

$3 p n^{- 4} \cdot (4 {nm}^{4} p^{3})$

Step 1

Multiply $p$ by $p^{3}$ by adding the exponents.

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Step 1.1

Move $p^{3}$ .

$3 (p^{3} p) n^{- 4} \cdot (4 {nm}^{4})$

Step 1.2

Multiply $p^{3}$ by $p$ .

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Step 1.2.1

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

$3 (p^{3} p^{1}) n^{- 4} \cdot (4 {nm}^{4})$

Step 1.2.2

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

$3 p^{3 + 1} n^{- 4} \cdot (4 {nm}^{4})$

Step 1.3

Add $3$ and $1$ .

$3 p^{4} n^{- 4} \cdot (4 {nm}^{4})$

Step 2

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

$3 p^{4} \frac{1}{n^{4}} \cdot (4 {nm}^{4})$

Step 3

Multiply $3 p^{4} \frac{1}{n^{4}}$ .

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Step 3.1

Combine $3$ and $\frac{1}{n^{4}}$ .

$p^{4} \frac{3}{n^{4}} \cdot (4 {nm}^{4})$

Step 3.2

Combine $p^{4}$ and $\frac{3}{n^{4}}$ .

$\frac{p^{4} \cdot 3}{n^{4}} \cdot (4 {nm}^{4})$

Step 4

Simplify.

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Step 4.1

Combine $\frac{p^{4} \cdot 3}{n^{4}}$ and $4 {nm}^{4}$ .

$\frac{p^{4} \cdot 3 \cdot 4}{n^{4}} {nm}^{4}$

Step 4.2

Multiply $4$ by $3$ .

$\frac{p^{4} \cdot 12}{n^{4}} {nm}^{4}$

Step 4.3

Move $12$ to the left of $p^{4}$ .

$\frac{12 p^{4}}{n^{4}} {nm}^{4}$