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

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

Step 1

Multiply $x^{- 4}$ by $x^{2}$ by adding the exponents.

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

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

Add $- 4$ and $2$ .

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

Step 2

Move $x^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 3

Move $y^{- 8}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{y^{3} x^{2} y^{8}}$

Step 4

Multiply $y^{3}$ by $y^{8}$ by adding the exponents.

Move $y^{8}$ .

$\frac{1}{y^{8} y^{3} x^{2}}$

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

$\frac{1}{y^{8 + 3} x^{2}}$

Add $8$ and $3$ .

$\frac{1}{y^{11} x^{2}}$