Algebra Examples

$x^{- 2} y^{- 1} \sqrt[3]{125 x^{4} y^{5}}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{x^{2}} y^{- 1} \sqrt[3]{125 x^{4} y^{5}}$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{x^{2}} \cdot \frac{1}{y} \sqrt[3]{125 x^{4} y^{5}}$

Step 3

Combine.

$\frac{1 \cdot 1}{x^{2} y} \sqrt[3]{125 x^{4} y^{5}}$

Step 4

Multiply $1$ by $1$ .

$\frac{1}{x^{2} y} \sqrt[3]{125 x^{4} y^{5}}$

Step 5

Rewrite $125 x^{4} y^{5}$ as ${(5 x y)}^{3} (x y^{2})$ .

Tap for more steps...

Step 5.1

Rewrite $125$ as $5^{3}$ .

$\frac{1}{x^{2} y} \sqrt[3]{5^{3} x^{4} y^{5}}$

Step 5.2

Factor out $x^{3}$ .

$\frac{1}{x^{2} y} \sqrt[3]{5^{3} (x^{3} x) y^{5}}$

Step 5.3

Factor out $y^{3}$ .

$\frac{1}{x^{2} y} \sqrt[3]{5^{3} (x^{3} x) (y^{3} y^{2})}$

Step 5.4

Move $x$ .

$\frac{1}{x^{2} y} \sqrt[3]{5^{3} (x^{3}) y^{3} x y^{2}}$

Step 5.5

Rewrite $5^{3} (x^{3}) y^{3}$ as ${(5 x y)}^{3}$ .

$\frac{1}{x^{2} y} \sqrt[3]{{(5 x y)}^{3} x y^{2}}$

Step 5.6

Add parentheses.

$\frac{1}{x^{2} y} \sqrt[3]{{(5 x y)}^{3} (x y^{2})}$

Step 6

Pull terms out from under the radical.

$\frac{1}{x^{2} y} (5 x y \sqrt[3]{x y^{2}})$

Step 7

Rewrite using the commutative property of multiplication.

$5 \frac{1}{x^{2} y} (x y \sqrt[3]{x y^{2}})$

Step 8

Combine $5$ and $\frac{1}{x^{2} y}$ .

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

Step 9

Cancel the common factor of $x y$ .

Tap for more steps...

Step 9.1

Factor $x y$ out of $x^{2} y$ .

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

Step 9.2

Factor $x y$ out of $x y \sqrt[3]{x y^{2}}$ .

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

Step 9.3

Cancel the common factor.

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

Step 9.4

Rewrite the expression.

$\frac{5}{x} \sqrt[3]{x y^{2}}$

Step 10

Combine $\frac{5}{x}$ and $\sqrt[3]{x y^{2}}$ .

$\frac{5 \sqrt[3]{x y^{2}}}{x}$