Simplify (x^-4y^-5y^2)/x

$\frac{x^{- 4} y^{- 5} y^{2}}{x}$

Step 1

Multiply $y^{- 5}$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

$\frac{x^{- 4} (y^{2} y^{- 5})}{x}$

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

$\frac{x^{- 4} y^{2 - 5}}{x}$

Subtract $5$ from $2$ .

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

Step 2

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

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

Step 3

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

$\frac{1}{x \cdot x^{4} y^{3}}$

Step 4

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

Multiply $x$ by $x^{4}$ .

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

$\frac{1}{x^{1} x^{4} y^{3}}$

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

$\frac{1}{x^{1 + 4} y^{3}}$

Add $1$ and $4$ .

$\frac{1}{x^{5} y^{3}}$