Simplify (-12x^5y^-2)/(8x^-3y)

$\frac{- 12 x^{5} y^{- 2}}{8 x^{- 3} y}$

Step 1

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

$\frac{- 12 x^{5}}{8 x^{- 3} y \cdot y^{2}}$

Step 2

Multiply $y$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

$\frac{- 12 x^{5}}{8 x^{- 3} (y^{2} y)}$

Multiply $y^{2}$ by $y$ .

Raise $y$ to the power of $1$ .

$\frac{- 12 x^{5}}{8 x^{- 3} (y^{2} y^{1})}$

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

$\frac{- 12 x^{5}}{8 x^{- 3} y^{2 + 1}}$

Add $2$ and $1$ .

$\frac{- 12 x^{5}}{8 x^{- 3} y^{3}}$

Step 3

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

$\frac{- 12 x^{5} x^{3}}{8 y^{3}}$

Step 4

Multiply $x^{5}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$\frac{- 12 (x^{3} x^{5})}{8 y^{3}}$

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

$\frac{- 12 x^{3 + 5}}{8 y^{3}}$

Add $3$ and $5$ .

$\frac{- 12 x^{8}}{8 y^{3}}$

Step 5

Cancel the common factor of $- 12$ and $8$ .

Factor $4$ out of $- 12 x^{8}$ .

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

Cancel the common factors.

Factor $4$ out of $8 y^{3}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 6

Move the negative in front of the fraction.

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