Simplify (10x^4y^9)/(30x^12y^-3)

$\frac{10 x^{4} y^{9}}{30 x^{12} y^{- 3}}$

Step 1

Move $y^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{10 x^{4} y^{9} y^{3}}{30 x^{12}}$

Step 2

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

Move $y^{3}$ .

$\frac{10 x^{4} (y^{3} y^{9})}{30 x^{12}}$

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

$\frac{10 x^{4} y^{3 + 9}}{30 x^{12}}$

Add $3$ and $9$ .

$\frac{10 x^{4} y^{12}}{30 x^{12}}$

Step 3

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

Factor $10$ out of $10 x^{4} y^{12}$ .

$\frac{10 (x^{4} y^{12})}{30 x^{12}}$

Cancel the common factors.

Factor $10$ out of $30 x^{12}$ .

$\frac{10 (x^{4} y^{12})}{10 (3 x^{12})}$

Cancel the common factor.

$\frac{10 (x^{4} y^{12})}{10 (3 x^{12})}$

Rewrite the expression.

$\frac{x^{4} y^{12}}{3 x^{12}}$

Step 4

Cancel the common factor of $x^{4}$ and $x^{12}$ .

Factor $x^{4}$ out of $x^{4} y^{12}$ .

$\frac{x^{4} (y^{12})}{3 x^{12}}$

Cancel the common factors.

Factor $x^{4}$ out of $3 x^{12}$ .

$\frac{x^{4} (y^{12})}{x^{4} (3 x^{8})}$

Cancel the common factor.

$\frac{x^{4} y^{12}}{x^{4} (3 x^{8})}$

Rewrite the expression.

$\frac{y^{12}}{3 x^{8}}$