Evaluate (x^-4x^-6y^2)/(y^6)

$\frac{x^{- 4} x^{- 6} y^{2}}{y^{6}}$

Step 1

Multiply $x^{- 4}$ by $x^{- 6}$ by adding the exponents.

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

$\frac{x^{- 4 - 6} y^{2}}{y^{6}}$

Subtract $6$ from $- 4$ .

$\frac{x^{- 10} y^{2}}{y^{6}}$

Step 2

Move $x^{- 10}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{y^{2}}{y^{6} x^{10}}$

Step 3

Cancel the common factor of $y^{2}$ and $y^{6}$ .

Multiply by $1$ .

$\frac{y^{2} \cdot 1}{y^{6} x^{10}}$

Cancel the common factors.

Factor $y^{2}$ out of $y^{6} x^{10}$ .

$\frac{y^{2} \cdot 1}{y^{2} (y^{4} x^{10})}$

Cancel the common factor.

$\frac{y^{2} \cdot 1}{y^{2} (y^{4} x^{10})}$

Rewrite the expression.

$\frac{1}{y^{4} x^{10}}$