Simplify (-5x^6y^2)^2-12x^12y^4

${(- 5 x^{6} y^{2})}^{2} - 12 x^{12} y^{4}$

Step 1

Simplify each term.

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

Apply the product rule to $- 5 x^{6} y^{2}$ .

${(- 5 x^{6})}^{2} {(y^{2})}^{2} - 12 x^{12} y^{4}$

Apply the product rule to $- 5 x^{6}$ .

${(- 5)}^{2} {(x^{6})}^{2} {(y^{2})}^{2} - 12 x^{12} y^{4}$

Raise $- 5$ to the power of $2$ .

$25 {(x^{6})}^{2} {(y^{2})}^{2} - 12 x^{12} y^{4}$

Multiply the exponents in ${(x^{6})}^{2}$ .

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

$25 x^{6 \cdot 2} {(y^{2})}^{2} - 12 x^{12} y^{4}$

Multiply $6$ by $2$ .

$25 x^{12} {(y^{2})}^{2} - 12 x^{12} y^{4}$

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

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

$25 x^{12} y^{2 \cdot 2} - 12 x^{12} y^{4}$

Multiply $2$ by $2$ .

$25 x^{12} y^{4} - 12 x^{12} y^{4}$

Step 2

Subtract $12 x^{12} y^{4}$ from $25 x^{12} y^{4}$ .

$13 x^{12} y^{4}$