Simplify (-15x^-2y^4)/(25x^2y)

$\frac{- 15 x^{- 2} y^{4}}{25 x^{2} y}$

Step 1

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

$\frac{- 15 y^{4}}{25 x^{2} y x^{2}}$

Step 2

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

Move $x^{2}$ .

$\frac{- 15 y^{4}}{25 (x^{2} x^{2}) y}$

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

$\frac{- 15 y^{4}}{25 x^{2 + 2} y}$

Add $2$ and $2$ .

$\frac{- 15 y^{4}}{25 x^{4} y}$

Step 3

Cancel the common factor of $- 15$ and $25$ .

Factor $5$ out of $- 15 y^{4}$ .

$\frac{5 (- 3 y^{4})}{25 x^{4} y}$

Cancel the common factors.

Factor $5$ out of $25 x^{4} y$ .

$\frac{5 (- 3 y^{4})}{5 (5 x^{4} y)}$

Cancel the common factor.

$\frac{5 (- 3 y^{4})}{5 (5 x^{4} y)}$

Rewrite the expression.

$\frac{- 3 y^{4}}{5 x^{4} y}$

Step 4

Cancel the common factor of $y^{4}$ and $y$ .

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

$\frac{y (- 3 y^{3})}{5 x^{4} y}$

Cancel the common factors.

Factor $y$ out of $5 x^{4} y$ .

$\frac{y (- 3 y^{3})}{y (5 x^{4})}$

Cancel the common factor.

$\frac{y (- 3 y^{3})}{y (5 x^{4})}$

Rewrite the expression.

$\frac{- 3 y^{3}}{5 x^{4}}$

Step 5

Move the negative in front of the fraction.

$- \frac{3 y^{3}}{5 x^{4}}$