Simplify (-2x^2y^6*4x^3y^6)^2

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

Step 1

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

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

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

${(- 2 x^{3 + 2} y^{6} \cdot (4 y^{6}))}^{2}$

Add $3$ and $2$ .

${(- 2 x^{5} y^{6} \cdot (4 y^{6}))}^{2}$

Step 2

Multiply $y^{6}$ by $y^{6}$ by adding the exponents.

Move $y^{6}$ .

${(- 2 x^{5} (y^{6} y^{6}) \cdot 4)}^{2}$

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

${(- 2 x^{5} y^{6 + 6} \cdot 4)}^{2}$

Add $6$ and $6$ .

${(- 2 x^{5} y^{12} \cdot 4)}^{2}$

Step 3

Multiply $4$ by $- 2$ .

${(- 8 x^{5} y^{12})}^{2}$

Step 4

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

Apply the product rule to $- 8 x^{5} y^{12}$ .

${(- 8 x^{5})}^{2} {(y^{12})}^{2}$

Apply the product rule to $- 8 x^{5}$ .

${(- 8)}^{2} {(x^{5})}^{2} {(y^{12})}^{2}$

Step 5

Raise $- 8$ to the power of $2$ .

$64 {(x^{5})}^{2} {(y^{12})}^{2}$

Step 6

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

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

$64 x^{5 \cdot 2} {(y^{12})}^{2}$

Multiply $5$ by $2$ .

$64 x^{10} {(y^{12})}^{2}$

Step 7

Multiply the exponents in ${(y^{12})}^{2}$ .

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

$64 x^{10} y^{12 \cdot 2}$

Multiply $12$ by $2$ .

$64 x^{10} y^{24}$