Simplify (-10g^6h^9(g^2h^3))/(30g^3h^3)

$\frac{- 10 g^{6} h^{9} (g^{2} h^{3})}{30 g^{3} h^{3}}$

Multiply $g^{6}$ by $g^{2}$ by adding the exponents.

Move $g^{2}$ .

$\frac{- 10 (g^{2} g^{6}) h^{9} h^{3}}{30 g^{3} h^{3}}$

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

$\frac{- 10 g^{2 + 6} h^{9} h^{3}}{30 g^{3} h^{3}}$

Add $2$ and $6$ .

$\frac{- 10 g^{8} h^{9} h^{3}}{30 g^{3} h^{3}}$

Multiply $h^{9}$ by $h^{3}$ by adding the exponents.

Move $h^{3}$ .

$\frac{- 10 g^{8} (h^{3} h^{9})}{30 g^{3} h^{3}}$

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

$\frac{- 10 g^{8} h^{3 + 9}}{30 g^{3} h^{3}}$

Add $3$ and $9$ .

$\frac{- 10 g^{8} h^{12}}{30 g^{3} h^{3}}$

Cancel the common factor of $- 10$ and $30$ .

Factor $10$ out of $- 10 g^{8} h^{12}$ .

$\frac{10 (- g^{8} h^{12})}{30 g^{3} h^{3}}$

Cancel the common factors.

Factor $10$ out of $30 g^{3} h^{3}$ .

$\frac{10 (- g^{8} h^{12})}{10 (3 g^{3} h^{3})}$

Cancel the common factor.

$\frac{10 (- g^{8} h^{12})}{10 (3 g^{3} h^{3})}$

Rewrite the expression.

$\frac{- g^{8} h^{12}}{3 g^{3} h^{3}}$

Cancel the common factor of $g^{8}$ and $g^{3}$ .

Factor $g^{3}$ out of $- g^{8} h^{12}$ .

$\frac{g^{3} (- g^{5} h^{12})}{3 g^{3} h^{3}}$

Cancel the common factors.

Factor $g^{3}$ out of $3 g^{3} h^{3}$ .

$\frac{g^{3} (- g^{5} h^{12})}{g^{3} (3 h^{3})}$

Cancel the common factor.

$\frac{g^{3} (- g^{5} h^{12})}{g^{3} (3 h^{3})}$

Rewrite the expression.

$\frac{- g^{5} h^{12}}{3 h^{3}}$

Cancel the common factor of $h^{12}$ and $h^{3}$ .

Factor $h^{3}$ out of $- g^{5} h^{12}$ .

$\frac{h^{3} (- g^{5} h^{9})}{3 h^{3}}$

Cancel the common factors.

Factor $h^{3}$ out of $3 h^{3}$ .

$\frac{h^{3} (- g^{5} h^{9})}{h^{3} \cdot 3}$

Cancel the common factor.

$\frac{h^{3} (- g^{5} h^{9})}{h^{3} \cdot 3}$

Rewrite the expression.

$\frac{- g^{5} h^{9}}{3}$

Move the negative in front of the fraction.

$- \frac{g^{5} h^{9}}{3}$

Simplify (-10g^6h^9(g^2h^3))/(30g^3h^3)

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