Simplify (x^-8y^-6y^5)/(x^-3)

$\frac{x^{- 8} y^{- 6} y^{5}}{x^{- 3}}$

Step 1

Multiply $y^{- 6}$ by $y^{5}$ by adding the exponents.

Move $y^{5}$ .

$\frac{x^{- 8} (y^{5} y^{- 6})}{x^{- 3}}$

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

$\frac{x^{- 8} y^{5 - 6}}{x^{- 3}}$

Subtract $6$ from $5$ .

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

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

Add $- 3$ and $8$ .

$\frac{1}{x^{5} y}$