Simplify (4xy)^2(4xy^2)

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

Step 1

Rewrite using the commutative property of multiplication.

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

Step 2

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

Apply the product rule to $4 x y$ .

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

Apply the product rule to $4 x$ .

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

Step 3

Multiply $4$ by $4^{2}$ by adding the exponents.

Move $4^{2}$ .

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

Multiply $4^{2}$ by $4$ .

Raise $4$ to the power of $1$ .

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

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

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

Add $2$ and $1$ .

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

Step 4

Multiply $x^{2}$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x^{2}$ .

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

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

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

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

Add $1$ and $2$ .

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

Step 5

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

Move $y^{2}$ .

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

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

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

Add $2$ and $2$ .

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

Step 6

Raise $4$ to the power of $3$ .

$64 x^{3} y^{4}$