Simplify (4x^4y)^2-11x^8y^2

${(4 x^{4} y)}^{2} - 11 x^{8} y^{2}$

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 $4 x^{4} y$ .

${(4 x^{4})}^{2} y^{2} - 11 x^{8} y^{2}$

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

$4^{2} {(x^{4})}^{2} y^{2} - 11 x^{8} y^{2}$

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

$16 {(x^{4})}^{2} y^{2} - 11 x^{8} y^{2}$

Multiply the exponents in ${(x^{4})}^{2}$ .

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

$16 x^{4 \cdot 2} y^{2} - 11 x^{8} y^{2}$

Multiply $4$ by $2$ .

$16 x^{8} y^{2} - 11 x^{8} y^{2}$

Step 2

Subtract $11 x^{8} y^{2}$ from $16 x^{8} y^{2}$ .

$5 x^{8} y^{2}$