Finite Math Examples

$\sqrt[6]{27 x y^{4}} \sqrt{3 x^{4} y}$

Step 1

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

Tap for more steps...

Step 1.1

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

$\sqrt[6]{27 x y^{4}} \sqrt{3 {(x^{2})}^{2} y}$

Step 1.2

Reorder $3$ and ${(x^{2})}^{2}$ .

$\sqrt[6]{27 x y^{4}} \sqrt{{(x^{2})}^{2} \cdot 3 y}$

Step 1.3

Add parentheses.

$\sqrt[6]{27 x y^{4}} \sqrt{{(x^{2})}^{2} \cdot (3 y)}$

Step 2

Pull terms out from under the radical.

$\sqrt[6]{27 x y^{4}} (x^{2} \sqrt{3 y})$

Step 3

Multiply $\sqrt[6]{27 x y^{4}} (x^{2} \sqrt{3 y})$ .

Tap for more steps...

Step 3.1

Rewrite the expression using the least common index of $6$ .

Tap for more steps...

Step 3.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 y}$ as ${(3 y)}^{\frac{1}{2}}$ .

$x^{2} (\sqrt[6]{27 x y^{4}} {(3 y)}^{\frac{1}{2}})$

Step 3.1.2

Rewrite ${(3 y)}^{\frac{1}{2}}$ as ${(3 y)}^{\frac{3}{6}}$ .

$x^{2} (\sqrt[6]{27 x y^{4}} {(3 y)}^{\frac{3}{6}})$

Step 3.1.3

Rewrite ${(3 y)}^{\frac{3}{6}}$ as $\sqrt[6]{{(3 y)}^{3}}$ .

$x^{2} (\sqrt[6]{27 x y^{4}} \sqrt[6]{{(3 y)}^{3}})$

Step 3.2

Combine using the product rule for radicals.

$x^{2} \sqrt[6]{27 x y^{4} {(3 y)}^{3}}$

Step 3.3

Apply the product rule to $3 y$ .

$x^{2} \sqrt[6]{27 x y^{4} \cdot 3^{3} y^{3}}$

Step 3.4

Combine exponents.

Tap for more steps...

Step 3.4.1

Rewrite $27$ as $3^{3}$ .

$x^{2} \sqrt[6]{3^{3} \cdot 3^{3} x y^{4} y^{3}}$

Step 3.4.2

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

$x^{2} \sqrt[6]{3^{3 + 3} x y^{4} y^{3}}$

Step 3.4.3

Add $3$ and $3$ .

$x^{2} \sqrt[6]{3^{6} x y^{4} y^{3}}$

Step 3.4.4

Multiply $y^{4}$ by $y^{3}$ by adding the exponents.

Tap for more steps...

Step 3.4.4.1

Move $y^{3}$ .

$x^{2} \sqrt[6]{3^{6} x (y^{3} y^{4})}$

Step 3.4.4.2

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

$x^{2} \sqrt[6]{3^{6} x y^{3 + 4}}$

Step 3.4.4.3

Add $3$ and $4$ .

$x^{2} \sqrt[6]{3^{6} x y^{7}}$

Step 3.5

Raise $3$ to the power of $6$ .

$x^{2} \sqrt[6]{729 x y^{7}}$

Step 4

Rewrite $729 x y^{7}$ as ${(3 y)}^{6} (x y)$ .

Tap for more steps...

Step 4.1

Rewrite $729$ as $3^{6}$ .

$x^{2} \sqrt[6]{3^{6} x y^{7}}$

Step 4.2

Factor out $y^{6}$ .

$x^{2} \sqrt[6]{3^{6} x (y^{6} y)}$

Step 4.3

Move $x$ .

$x^{2} \sqrt[6]{3^{6} y^{6} x y}$

Step 4.4

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

$x^{2} \sqrt[6]{{(3 y)}^{6} x y}$

Step 4.5

Add parentheses.

$x^{2} \sqrt[6]{{(3 y)}^{6} (x y)}$

Step 5

Pull terms out from under the radical.

$x^{2} (3 y \sqrt[6]{x y})$

Step 6

Rewrite using the commutative property of multiplication.

$3 x^{2} y \sqrt[6]{x y}$