Algebra Examples

$5 y \sqrt{4 x^{4} y^{6}}$

Step 1

Rewrite $4 x^{4} y^{6}$ as ${(2 x^{2} y^{3})}^{2}$ .

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

Step 2

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

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

Step 3

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

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Step 3.1

Move $y^{3}$ .

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

Step 3.2

Multiply $y^{3}$ by $y$ .

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Step 3.2.1

Raise $y$ to the power of $1$ .

$5 (y^{3} y^{1}) (2 x^{2})$

Step 3.2.2

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

$5 y^{3 + 1} (2 x^{2})$

Step 3.3

Add $3$ and $1$ .

$5 y^{4} (2 x^{2})$

Step 4

Rewrite using the commutative property of multiplication.

$5 \cdot 2 y^{4} x^{2}$

Step 5

Multiply $5$ by $2$ .

$10 y^{4} x^{2}$