Simplify xy^3 square root of 25x^2y^4

$x y^{3} \sqrt{25 x^{2} y^{4}}$

Step 1

Rewrite $25 x^{2} y^{4}$ as ${(5 x y^{2})}^{2}$ .

$x y^{3} \sqrt{{(5 x y^{2})}^{2}}$

Step 2

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

$x y^{3} (5 x y^{2})$

Step 3

Rewrite using the commutative property of multiplication.

$5 x y^{3} (x y^{2})$

Step 4

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$5 (x \cdot x) y^{3} y^{2}$

Multiply $x$ by $x$ .

$5 x^{2} y^{3} y^{2}$

Step 5

Multiply $y^{3}$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

$5 x^{2} (y^{2} y^{3})$

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

$5 x^{2} y^{2 + 3}$

Add $2$ and $3$ .

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