Simplify square root of a^4* square root of 81b^4

$\sqrt{a^{4}} \cdot \sqrt{81 b^{4}}$

Step 1

Rewrite $a^{4}$ as ${(a^{2})}^{2}$ .

$\sqrt{{(a^{2})}^{2}} \cdot \sqrt{81 b^{4}}$

Step 2

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

$a^{2} \cdot \sqrt{81 b^{4}}$

Step 3

Rewrite $81 b^{4}$ as ${(9 b^{2})}^{2}$ .

$a^{2} \cdot \sqrt{{(9 b^{2})}^{2}}$

Step 4

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

$a^{2} \cdot (9 b^{2})$

Step 5

Rewrite using the commutative property of multiplication.

$9 a^{2} b^{2}$