Simplify (x^2y^-4y^-8)/(x^3)

$\frac{x^{2} y^{- 4} y^{- 8}}{x^{3}}$

Step 1

Multiply $y^{- 4}$ by $y^{- 8}$ by adding the exponents.

Move $y^{- 8}$ .

$\frac{x^{2} (y^{- 8} y^{- 4})}{x^{3}}$

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

$\frac{x^{2} y^{- 8 - 4}}{x^{3}}$

Subtract $4$ from $- 8$ .

$\frac{x^{2} y^{- 12}}{x^{3}}$

Step 2

Move $y^{- 12}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{x^{2}}{x^{3} y^{12}}$

Step 3

Cancel the common factor of $x^{2}$ and $x^{3}$ .

Multiply by $1$ .

$\frac{x^{2} \cdot 1}{x^{3} y^{12}}$

Cancel the common factors.

Factor $x^{2}$ out of $x^{3} y^{12}$ .

$\frac{x^{2} \cdot 1}{x^{2} (x y^{12})}$

Cancel the common factor.

$\frac{x^{2} \cdot 1}{x^{2} (x y^{12})}$

Rewrite the expression.

$\frac{1}{x y^{12}}$