Simplify square root of (11y^2)^4

$\sqrt{{(11 y^{2})}^{4}}$

Simplify the expression.

Apply the product rule to $11 y^{2}$ .

$\sqrt{11^{4} {(y^{2})}^{4}}$

Raise $11$ to the power of $4$ .

$\sqrt{14641 {(y^{2})}^{4}}$

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

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

$\sqrt{14641 y^{2 \cdot 4}}$

Multiply $2$ by $4$ .

$\sqrt{14641 y^{8}}$

Rewrite $14641 y^{8}$ as ${(121 y^{4})}^{2}$ .

$\sqrt{{(121 y^{4})}^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$121 y^{4}$