Simplify (x^-1)/((xy)^3)

$\frac{x^{- 1}}{{(x y)}^{3}}$

Step 1

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

$\frac{1}{{(x y)}^{3} x}$

Step 2

Simplify the denominator.

Apply the product rule to $x y$ .

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

Combine exponents.

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

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

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

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

Add $1$ and $3$ .

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