Algebra Examples

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

Step 1

Simplify the expression.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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Step 1.3.1

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

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

Step 1.3.2

Multiply $2$ by $4$ .

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

Step 2

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

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

Step 3

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

$121 y^{4}$