Simplify (-12n^7p^5(n^2p^4))/(36n^6p^7)

$\frac{- 12 n^{7} p^{5} (n^{2} p^{4})}{36 n^{6} p^{7}}$

Step 1

Multiply $n^{7}$ by $n^{2}$ by adding the exponents.

Move $n^{2}$ .

$\frac{- 12 (n^{2} n^{7}) p^{5} p^{4}}{36 n^{6} p^{7}}$

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

$\frac{- 12 n^{2 + 7} p^{5} p^{4}}{36 n^{6} p^{7}}$

Add $2$ and $7$ .

$\frac{- 12 n^{9} p^{5} p^{4}}{36 n^{6} p^{7}}$

Step 2

Multiply $p^{5}$ by $p^{4}$ by adding the exponents.

Move $p^{4}$ .

$\frac{- 12 n^{9} (p^{4} p^{5})}{36 n^{6} p^{7}}$

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

$\frac{- 12 n^{9} p^{4 + 5}}{36 n^{6} p^{7}}$

Add $4$ and $5$ .

$\frac{- 12 n^{9} p^{9}}{36 n^{6} p^{7}}$

Step 3

Cancel the common factor of $- 12$ and $36$ .

Factor $12$ out of $- 12 n^{9} p^{9}$ .

$\frac{12 (- n^{9} p^{9})}{36 n^{6} p^{7}}$

Cancel the common factors.

Factor $12$ out of $36 n^{6} p^{7}$ .

$\frac{12 (- n^{9} p^{9})}{12 (3 n^{6} p^{7})}$

Cancel the common factor.

$\frac{12 (- n^{9} p^{9})}{12 (3 n^{6} p^{7})}$

Rewrite the expression.

$\frac{- n^{9} p^{9}}{3 n^{6} p^{7}}$

Step 4

Cancel the common factor of $n^{9}$ and $n^{6}$ .

Factor $n^{6}$ out of $- n^{9} p^{9}$ .

$\frac{n^{6} (- n^{3} p^{9})}{3 n^{6} p^{7}}$

Cancel the common factors.

Factor $n^{6}$ out of $3 n^{6} p^{7}$ .

$\frac{n^{6} (- n^{3} p^{9})}{n^{6} (3 p^{7})}$

Cancel the common factor.

$\frac{n^{6} (- n^{3} p^{9})}{n^{6} (3 p^{7})}$

Rewrite the expression.

$\frac{- n^{3} p^{9}}{3 p^{7}}$

Step 5

Cancel the common factor of $p^{9}$ and $p^{7}$ .

Factor $p^{7}$ out of $- n^{3} p^{9}$ .

$\frac{p^{7} (- n^{3} p^{2})}{3 p^{7}}$

Cancel the common factors.

Factor $p^{7}$ out of $3 p^{7}$ .

$\frac{p^{7} (- n^{3} p^{2})}{p^{7} \cdot 3}$

Cancel the common factor.

$\frac{p^{7} (- n^{3} p^{2})}{p^{7} \cdot 3}$

Rewrite the expression.

$\frac{- n^{3} p^{2}}{3}$

Step 6

Move the negative in front of the fraction.

$- \frac{n^{3} p^{2}}{3}$

Simplify (-12n^7p^5(n^2p^4))/(36n^6p^7)

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