Simplify (8x^-3y^-1)/(-2x^6y^-4)

$\frac{8 x^{- 3} y^{- 1}}{- 2 x^{6} y^{- 4}}$

Step 1

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

$\frac{8 y^{- 1}}{- 2 x^{6} y^{- 4} x^{3}}$

Step 2

Multiply $x^{6}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$\frac{8 y^{- 1}}{- 2 (x^{3} x^{6}) y^{- 4}}$

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

$\frac{8 y^{- 1}}{- 2 x^{3 + 6} y^{- 4}}$

Add $3$ and $6$ .

$\frac{8 y^{- 1}}{- 2 x^{9} y^{- 4}}$

Step 3

Move $y^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{8 y^{- 1} y^{4}}{- 2 x^{9}}$

Step 4

Multiply $y^{- 1}$ by $y^{4}$ by adding the exponents.

Move $y^{4}$ .

$\frac{8 (y^{4} y^{- 1})}{- 2 x^{9}}$

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

$\frac{8 y^{4 - 1}}{- 2 x^{9}}$

Subtract $1$ from $4$ .

$\frac{8 y^{3}}{- 2 x^{9}}$

Step 5

Cancel the common factor of $8$ and $- 2$ .

Factor $2$ out of $8 y^{3}$ .

$\frac{2 (4 y^{3})}{- 2 x^{9}}$

Cancel the common factors.

Factor $2$ out of $- 2 x^{9}$ .

$\frac{2 (4 y^{3})}{2 (- x^{9})}$

Cancel the common factor.

$\frac{2 (4 y^{3})}{2 (- x^{9})}$

Rewrite the expression.

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

Step 6

Move the negative in front of the fraction.

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