Simplify (((4x^2y^3)^3)/((2xy)^4))^2

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

Simplify the numerator.

Apply the product rule to $4 x^{2} y^{3}$ .

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

Apply the product rule to $4 x^{2}$ .

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

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

${(\frac{64 {(x^{2})}^{3} {(y^{3})}^{3}}{{(2 x y)}^{4}})}^{2}$

Multiply the exponents in ${(x^{2})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(\frac{64 x^{2 \cdot 3} {(y^{3})}^{3}}{{(2 x y)}^{4}})}^{2}$

Multiply $2$ by $3$ .

${(\frac{64 x^{6} {(y^{3})}^{3}}{{(2 x y)}^{4}})}^{2}$

Multiply the exponents in ${(y^{3})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(\frac{64 x^{6} y^{3 \cdot 3}}{{(2 x y)}^{4}})}^{2}$

Multiply $3$ by $3$ .

${(\frac{64 x^{6} y^{9}}{{(2 x y)}^{4}})}^{2}$

Simplify the denominator.

Apply the product rule to $2 x y$ .

${(\frac{64 x^{6} y^{9}}{{(2 x)}^{4} y^{4}})}^{2}$

Apply the product rule to $2 x$ .

${(\frac{64 x^{6} y^{9}}{2^{4} x^{4} y^{4}})}^{2}$

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

${(\frac{64 x^{6} y^{9}}{16 x^{4} y^{4}})}^{2}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $64$ and $16$ .

Factor $16$ out of $64 x^{6} y^{9}$ .

${(\frac{16 (4 x^{6} y^{9})}{16 x^{4} y^{4}})}^{2}$

Cancel the common factors.

Factor $16$ out of $16 x^{4} y^{4}$ .

${(\frac{16 (4 x^{6} y^{9})}{16 (x^{4} y^{4})})}^{2}$

Cancel the common factor.

${(\frac{16 (4 x^{6} y^{9})}{16 (x^{4} y^{4})})}^{2}$

Rewrite the expression.

${(\frac{4 x^{6} y^{9}}{x^{4} y^{4}})}^{2}$

Cancel the common factor of $x^{6}$ and $x^{4}$ .

Factor $x^{4}$ out of $4 x^{6} y^{9}$ .

${(\frac{x^{4} (4 x^{2} y^{9})}{x^{4} y^{4}})}^{2}$

Cancel the common factors.

Factor $x^{4}$ out of $x^{4} y^{4}$ .

${(\frac{x^{4} (4 x^{2} y^{9})}{x^{4} (y^{4})})}^{2}$

Cancel the common factor.

${(\frac{x^{4} (4 x^{2} y^{9})}{x^{4} y^{4}})}^{2}$

Rewrite the expression.

${(\frac{4 x^{2} y^{9}}{y^{4}})}^{2}$

Cancel the common factor of $y^{9}$ and $y^{4}$ .

Factor $y^{4}$ out of $4 x^{2} y^{9}$ .

${(\frac{y^{4} (4 x^{2} y^{5})}{y^{4}})}^{2}$

Cancel the common factors.

Multiply by $1$ .

${(\frac{y^{4} (4 x^{2} y^{5})}{y^{4} \cdot 1})}^{2}$

Cancel the common factor.

${(\frac{y^{4} (4 x^{2} y^{5})}{y^{4} \cdot 1})}^{2}$

Rewrite the expression.

${(\frac{4 x^{2} y^{5}}{1})}^{2}$

Divide $4 x^{2} y^{5}$ by $1$ .

${(4 x^{2} y^{5})}^{2}$

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

Apply the product rule to $4 x^{2} y^{5}$ .

${(4 x^{2})}^{2} {(y^{5})}^{2}$

Apply the product rule to $4 x^{2}$ .

$4^{2} {(x^{2})}^{2} {(y^{5})}^{2}$

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

$16 {(x^{2})}^{2} {(y^{5})}^{2}$

Multiply the exponents in ${(x^{2})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$16 x^{2 \cdot 2} {(y^{5})}^{2}$

Multiply $2$ by $2$ .

$16 x^{4} {(y^{5})}^{2}$

Multiply the exponents in ${(y^{5})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$16 x^{4} y^{5 \cdot 2}$

Multiply $5$ by $2$ .

$16 x^{4} y^{10}$

Simplify (((4x^2y^3)^3)/((2xy)^4))^2

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