Simplify ((6u^11v^6)(11u^5v))/(-44u^11v^12)

$\frac{(6 u^{11} v^{6}) (11 u^{5} v)}{- 44 u^{11} v^{12}}$

Step 1

Multiply $u^{11}$ by $u^{5}$ by adding the exponents.

Move $u^{5}$ .

$\frac{6 (u^{5} u^{11}) v^{6} (11 v)}{- 44 u^{11} v^{12}}$

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

$\frac{6 u^{5 + 11} v^{6} (11 v)}{- 44 u^{11} v^{12}}$

Add $5$ and $11$ .

$\frac{6 u^{16} v^{6} (11 v)}{- 44 u^{11} v^{12}}$

Step 2

Multiply $v^{6}$ by $v$ by adding the exponents.

Move $v$ .

$\frac{6 u^{16} (v \cdot v^{6}) \cdot 11}{- 44 u^{11} v^{12}}$

Multiply $v$ by $v^{6}$ .

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

$\frac{6 u^{16} (v^{1} v^{6}) \cdot 11}{- 44 u^{11} v^{12}}$

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

$\frac{6 u^{16} v^{1 + 6} \cdot 11}{- 44 u^{11} v^{12}}$

Add $1$ and $6$ .

$\frac{6 u^{16} v^{7} \cdot 11}{- 44 u^{11} v^{12}}$

Step 3

Cancel the common factor of $6$ and $- 44$ .

Factor $2$ out of $6 u^{16} v^{7} \cdot 11$ .

$\frac{2 (3 u^{16} v^{7} \cdot 11)}{- 44 u^{11} v^{12}}$

Cancel the common factors.

Factor $2$ out of $- 44 u^{11} v^{12}$ .

$\frac{2 (3 u^{16} v^{7} \cdot 11)}{2 (- 22 u^{11} v^{12})}$

Cancel the common factor.

$\frac{2 (3 u^{16} v^{7} \cdot 11)}{2 (- 22 u^{11} v^{12})}$

Rewrite the expression.

$\frac{3 u^{16} v^{7} \cdot 11}{- 22 u^{11} v^{12}}$

Step 4

Cancel the common factor of $u^{16}$ and $u^{11}$ .

Factor $u^{11}$ out of $3 u^{16} v^{7} \cdot 11$ .

$\frac{u^{11} (3 u^{5} v^{7} \cdot 11)}{- 22 u^{11} v^{12}}$

Cancel the common factors.

Factor $u^{11}$ out of $- 22 u^{11} v^{12}$ .

$\frac{u^{11} (3 u^{5} v^{7} \cdot 11)}{u^{11} (- 22 v^{12})}$

Cancel the common factor.

$\frac{u^{11} (3 u^{5} v^{7} \cdot 11)}{u^{11} (- 22 v^{12})}$

Rewrite the expression.

$\frac{3 u^{5} v^{7} \cdot 11}{- 22 v^{12}}$

Step 5

Cancel the common factor of $v^{7}$ and $v^{12}$ .

Factor $v^{7}$ out of $3 u^{5} v^{7} \cdot 11$ .

$\frac{v^{7} (3 u^{5} \cdot 11)}{- 22 v^{12}}$

Cancel the common factors.

Factor $v^{7}$ out of $- 22 v^{12}$ .

$\frac{v^{7} (3 u^{5} \cdot 11)}{v^{7} (- 22 v^{5})}$

Cancel the common factor.

$\frac{v^{7} (3 u^{5} \cdot 11)}{v^{7} (- 22 v^{5})}$

Rewrite the expression.

$\frac{3 u^{5} \cdot 11}{- 22 v^{5}}$

Step 6

Cancel the common factor of $11$ and $- 22$ .

Factor $11$ out of $3 u^{5} \cdot 11$ .

$\frac{11 \cdot (3 u^{5})}{- 22 v^{5}}$

Cancel the common factors.

Factor $11$ out of $- 22 v^{5}$ .

$\frac{11 \cdot (3 u^{5})}{11 (- 2 v^{5})}$

Cancel the common factor.

$\frac{11 \cdot (3 u^{5})}{11 (- 2 v^{5})}$

Rewrite the expression.

$\frac{3 u^{5}}{- 2 v^{5}}$

Step 7

Move the negative in front of the fraction.

$- \frac{3 u^{5}}{2 v^{5}}$

Simplify ((6u^11v^6)(11u^5v))/(-44u^11v^12)

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