Simplify (12a^11b^2)/((14a^9b^10)(2a^10b^9))

$\frac{12 a^{11} b^{2}}{(14 a^{9} b^{10}) (2 a^{10} b^{9})}$

Step 1

Multiply $a^{9}$ by $a^{10}$ by adding the exponents.

Move $a^{10}$ .

$\frac{12 a^{11} b^{2}}{14 (a^{10} a^{9}) b^{10} (2 b^{9})}$

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

$\frac{12 a^{11} b^{2}}{14 a^{10 + 9} b^{10} (2 b^{9})}$

Add $10$ and $9$ .

$\frac{12 a^{11} b^{2}}{14 a^{19} b^{10} (2 b^{9})}$

Step 2

Multiply $b^{10}$ by $b^{9}$ by adding the exponents.

Move $b^{9}$ .

$\frac{12 a^{11} b^{2}}{14 a^{19} (b^{9} b^{10}) \cdot 2}$

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

$\frac{12 a^{11} b^{2}}{14 a^{19} b^{9 + 10} \cdot 2}$

Add $9$ and $10$ .

$\frac{12 a^{11} b^{2}}{14 a^{19} b^{19} \cdot 2}$

Step 3

Cancel the common factor of $12$ and $14$ .

Factor $2$ out of $12 a^{11} b^{2}$ .

$\frac{2 (6 a^{11} b^{2})}{14 a^{19} b^{19} \cdot 2}$

Cancel the common factors.

Factor $2$ out of $14 a^{19} b^{19} \cdot 2$ .

$\frac{2 (6 a^{11} b^{2})}{2 (7 a^{19} b^{19} \cdot 2)}$

Cancel the common factor.

$\frac{2 (6 a^{11} b^{2})}{2 (7 a^{19} b^{19} \cdot 2)}$

Rewrite the expression.

$\frac{6 a^{11} b^{2}}{7 a^{19} b^{19} \cdot 2}$

Step 4

Cancel the common factor of $6$ and $2$ .

Factor $2$ out of $6 a^{11} b^{2}$ .

$\frac{2 (3 a^{11} b^{2})}{7 a^{19} b^{19} \cdot 2}$

Cancel the common factors.

Factor $2$ out of $7 a^{19} b^{19} \cdot 2$ .

$\frac{2 (3 a^{11} b^{2})}{2 \cdot (7 a^{19} b^{19})}$

Cancel the common factor.

$\frac{2 (3 a^{11} b^{2})}{2 \cdot (7 a^{19} b^{19})}$

Rewrite the expression.

$\frac{3 a^{11} b^{2}}{7 a^{19} b^{19}}$

Step 5

Cancel the common factor of $a^{11}$ and $a^{19}$ .

Factor $a^{11}$ out of $3 a^{11} b^{2}$ .

$\frac{a^{11} (3 b^{2})}{7 a^{19} b^{19}}$

Cancel the common factors.

Factor $a^{11}$ out of $7 a^{19} b^{19}$ .

$\frac{a^{11} (3 b^{2})}{a^{11} (7 a^{8} b^{19})}$

Cancel the common factor.

$\frac{a^{11} (3 b^{2})}{a^{11} (7 a^{8} b^{19})}$

Rewrite the expression.

$\frac{3 b^{2}}{7 a^{8} b^{19}}$

Step 6

Cancel the common factor of $b^{2}$ and $b^{19}$ .

Factor $b^{2}$ out of $3 b^{2}$ .

$\frac{b^{2} \cdot 3}{7 a^{8} b^{19}}$

Cancel the common factors.

Factor $b^{2}$ out of $7 a^{8} b^{19}$ .

$\frac{b^{2} \cdot 3}{b^{2} (7 a^{8} b^{17})}$

Cancel the common factor.

$\frac{b^{2} \cdot 3}{b^{2} (7 a^{8} b^{17})}$

Rewrite the expression.

$\frac{3}{7 a^{8} b^{17}}$

Simplify (12a^11b^2)/((14a^9b^10)(2a^10b^9))

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