Simplify 1/4xy(4xy)^3

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

Step 1

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

Apply the product rule to $4 x y$ .

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

Apply the product rule to $4 x$ .

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

Step 2

Cancel the common factor of $4$ .

Factor $4$ out of $x y (4^{3} x^{3} y^{3})$ .

$\frac{1}{4} \cdot (4 (x y (4^{2} x^{3} y^{3})))$

Cancel the common factor.

$\frac{1}{4} \cdot (4 (x y (4^{2} x^{3} y^{3})))$

Rewrite the expression.

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

Step 3

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

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

Step 4

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

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

Step 5

Add $3$ and $1$ .

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

Step 6

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

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

Step 7

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

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

Step 8

Add $1$ and $3$ .

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

Step 9

Rewrite using the commutative property of multiplication.

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

Step 10

Raise $4$ to the power of $2$ .

$16 x^{4} y^{4}$