Simplify square root of (9y^2)^2 square root of (9y^2)^2

$\sqrt{{(9 y^{2})}^{2}} \sqrt{{(9 y^{2})}^{2}}$

Step 1

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

$9 y^{2} \sqrt{{(9 y^{2})}^{2}}$

Step 2

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

$9 y^{2} (9 y^{2})$

Step 3

Rewrite using the commutative property of multiplication.

$9 \cdot 9 y^{2} y^{2}$

Step 4

Multiply $y^{2}$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

$9 \cdot 9 (y^{2} y^{2})$

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

$9 \cdot 9 y^{2 + 2}$

Add $2$ and $2$ .

$9 \cdot 9 y^{4}$

Step 5

Multiply $9$ by $9$ .

$81 y^{4}$