Simplify (xy^-6)(xy)^3

$(x y^{- 6}) {(x y)}^{3}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$x \frac{1}{y^{6}} {(x y)}^{3}$

Step 2

Combine $x$ and $\frac{1}{y^{6}}$ .

$\frac{x}{y^{6}} {(x y)}^{3}$

Step 3

Apply the product rule to $x y$ .

$\frac{x}{y^{6}} (x^{3} y^{3})$

Step 4

Cancel the common factor of $y^{3}$ .

Factor $y^{3}$ out of $y^{6}$ .

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

Factor $y^{3}$ out of $x^{3} y^{3}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 5

Combine $\frac{x}{y^{3}}$ and $x^{3}$ .

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

Step 6

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

Multiply $x$ by $x^{3}$ .

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

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

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

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

Add $1$ and $3$ .

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