Simplify 1/6xy(6xy)^3

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

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $6 x y$ .

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

Apply the product rule to $6 x$ .

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

Cancel the common factor of $6$ .

Factor $6$ out of $x y (6^{3} x^{3} y^{3})$ .

$\frac{1}{6} \cdot (6 (x y (6^{2} x^{3} y^{3})))$

Cancel the common factor.

$\frac{1}{6} \cdot (6 (x y (6^{2} x^{3} y^{3})))$

Rewrite the expression.

$x y (6^{2} x^{3} y^{3})$

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

$x^{3} x^{1} y (6^{2} y^{3})$

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

$x^{3 + 1} y (6^{2} y^{3})$

Add $3$ and $1$ .

$x^{4} y (6^{2} y^{3})$

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

$x^{4} (6^{2} (y^{1} y^{3}))$

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

$x^{4} (6^{2} y^{1 + 3})$

Add $1$ and $3$ .

$x^{4} (6^{2} y^{4})$

Rewrite using the commutative property of multiplication.

$6^{2} x^{4} y^{4}$

Raise $6$ to the power of $2$ .

$36 x^{4} y^{4}$