Algebra Examples

$\sqrt[3]{3 x^{2} b} \div \sqrt[3]{25 x y^{2}}$

Step 1

Rewrite the division as a fraction.

$\frac{\sqrt[3]{3 x^{2} b}}{\sqrt[3]{25 x y^{2}}}$

Step 2

Combine $\sqrt[3]{3 x^{2} b}$ and $\sqrt[3]{25 x y^{2}}$ into a single radical.

$\sqrt[3]{\frac{3 x^{2} b}{25 x y^{2}}}$

Step 3

Reduce the expression $\frac{3 x^{2} b}{25 x y^{2}}$ by cancelling the common factors.

Tap for more steps...

Step 3.1

Factor $x$ out of $3 x^{2} b$ .

$\sqrt[3]{\frac{x (3 x b)}{25 x y^{2}}}$

Step 3.2

Factor $x$ out of $25 x y^{2}$ .

$\sqrt[3]{\frac{x (3 x b)}{x (25 y^{2})}}$

Step 3.3

Cancel the common factor.

$\sqrt[3]{\frac{x (3 x b)}{x (25 y^{2})}}$

Step 3.4

Rewrite the expression.

$\sqrt[3]{\frac{3 x b}{25 y^{2}}}$

Step 4

Rewrite $\sqrt[3]{\frac{3 x b}{25 y^{2}}}$ as $\frac{\sqrt[3]{3 x b}}{\sqrt[3]{25 y^{2}}}$ .

$\frac{\sqrt[3]{3 x b}}{\sqrt[3]{25 y^{2}}}$

Step 5

Multiply $\frac{\sqrt[3]{3 x b}}{\sqrt[3]{25 y^{2}}}$ by $\frac{{\sqrt[3]{25 y^{2}}}^{2}}{{\sqrt[3]{25 y^{2}}}^{2}}$ .

$\frac{\sqrt[3]{3 x b}}{\sqrt[3]{25 y^{2}}} \cdot \frac{{\sqrt[3]{25 y^{2}}}^{2}}{{\sqrt[3]{25 y^{2}}}^{2}}$

Step 6

Combine and simplify the denominator.

Tap for more steps...

Step 6.1

Multiply $\frac{\sqrt[3]{3 x b}}{\sqrt[3]{25 y^{2}}}$ by $\frac{{\sqrt[3]{25 y^{2}}}^{2}}{{\sqrt[3]{25 y^{2}}}^{2}}$ .

$\frac{\sqrt[3]{3 x b} {\sqrt[3]{25 y^{2}}}^{2}}{\sqrt[3]{25 y^{2}} {\sqrt[3]{25 y^{2}}}^{2}}$

Step 6.2

Raise $\sqrt[3]{25 y^{2}}$ to the power of $1$ .

$\frac{\sqrt[3]{3 x b} {\sqrt[3]{25 y^{2}}}^{2}}{{\sqrt[3]{25 y^{2}}}^{1} {\sqrt[3]{25 y^{2}}}^{2}}$

Step 6.3

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

$\frac{\sqrt[3]{3 x b} {\sqrt[3]{25 y^{2}}}^{2}}{{\sqrt[3]{25 y^{2}}}^{1 + 2}}$

Step 6.4

Add $1$ and $2$ .

$\frac{\sqrt[3]{3 x b} {\sqrt[3]{25 y^{2}}}^{2}}{{\sqrt[3]{25 y^{2}}}^{3}}$

Step 6.5

Rewrite ${\sqrt[3]{25 y^{2}}}^{3}$ as $25 y^{2}$ .

Tap for more steps...

Step 6.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{25 y^{2}}$ as ${(25 y^{2})}^{\frac{1}{3}}$ .

$\frac{\sqrt[3]{3 x b} {\sqrt[3]{25 y^{2}}}^{2}}{{({(25 y^{2})}^{\frac{1}{3}})}^{3}}$

Step 6.5.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{\sqrt[3]{3 x b} {\sqrt[3]{25 y^{2}}}^{2}}{{(25 y^{2})}^{\frac{1}{3} \cdot 3}}$

Step 6.5.3

Combine $\frac{1}{3}$ and $3$ .

$\frac{\sqrt[3]{3 x b} {\sqrt[3]{25 y^{2}}}^{2}}{{(25 y^{2})}^{\frac{3}{3}}}$

Step 6.5.4

Cancel the common factor of $3$ .

Tap for more steps...

Step 6.5.4.1

Cancel the common factor.

$\frac{\sqrt[3]{3 x b} {\sqrt[3]{25 y^{2}}}^{2}}{{(25 y^{2})}^{\frac{3}{3}}}$

Step 6.5.4.2

Rewrite the expression.

$\frac{\sqrt[3]{3 x b} {\sqrt[3]{25 y^{2}}}^{2}}{{(25 y^{2})}^{1}}$

Step 6.5.5

Simplify.

$\frac{\sqrt[3]{3 x b} {\sqrt[3]{25 y^{2}}}^{2}}{25 y^{2}}$

Step 7

Simplify the numerator.

Tap for more steps...

Step 7.1

Rewrite ${\sqrt[3]{25 y^{2}}}^{2}$ as $\sqrt[3]{{(25 y^{2})}^{2}}$ .

$\frac{\sqrt[3]{3 x b} \sqrt[3]{{(25 y^{2})}^{2}}}{25 y^{2}}$

Step 7.2

Apply the product rule to $25 y^{2}$ .

$\frac{\sqrt[3]{3 x b} \sqrt[3]{25^{2} {(y^{2})}^{2}}}{25 y^{2}}$

Step 7.3

Raise $25$ to the power of $2$ .

$\frac{\sqrt[3]{3 x b} \sqrt[3]{625 {(y^{2})}^{2}}}{25 y^{2}}$

Step 7.4

Multiply the exponents in ${(y^{2})}^{2}$ .

Tap for more steps...

Step 7.4.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{\sqrt[3]{3 x b} \sqrt[3]{625 y^{2 \cdot 2}}}{25 y^{2}}$

Step 7.4.2

Multiply $2$ by $2$ .

$\frac{\sqrt[3]{3 x b} \sqrt[3]{625 y^{4}}}{25 y^{2}}$

Step 7.5

Rewrite $625 y^{4}$ as ${(5 y)}^{3} \cdot (5 y)$ .

Tap for more steps...

Step 7.5.1

Factor $125$ out of $625$ .

$\frac{\sqrt[3]{3 x b} \sqrt[3]{125 (5) y^{4}}}{25 y^{2}}$

Step 7.5.2

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

$\frac{\sqrt[3]{3 x b} \sqrt[3]{5^{3} \cdot 5 y^{4}}}{25 y^{2}}$

Step 7.5.3

Factor out $y^{3}$ .

$\frac{\sqrt[3]{3 x b} \sqrt[3]{5^{3} \cdot 5 (y^{3} y)}}{25 y^{2}}$

Step 7.5.4

Move $5$ .

$\frac{\sqrt[3]{3 x b} \sqrt[3]{5^{3} y^{3} \cdot 5 y}}{25 y^{2}}$

Step 7.5.5

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

$\frac{\sqrt[3]{3 x b} \sqrt[3]{{(5 y)}^{3} \cdot 5 y}}{25 y^{2}}$

Step 7.5.6

Add parentheses.

$\frac{\sqrt[3]{3 x b} \sqrt[3]{{(5 y)}^{3} \cdot (5 y)}}{25 y^{2}}$

Step 7.6

Pull terms out from under the radical.

$\frac{\sqrt[3]{3 x b} \cdot 5 y \sqrt[3]{5 y}}{25 y^{2}}$

Step 7.7

Combine exponents.

Tap for more steps...

Step 7.7.1

Combine using the product rule for radicals.

$\frac{5 y \sqrt[3]{3 x b (5 y)}}{25 y^{2}}$

Step 7.7.2

Multiply $5$ by $3$ .

$\frac{5 y \sqrt[3]{15 x b y}}{25 y^{2}}$

Step 8

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 8.1

Cancel the common factor of $5$ and $25$ .

Tap for more steps...

Step 8.1.1

Factor $5$ out of $5 y \sqrt[3]{15 x b y}$ .

$\frac{5 (y \sqrt[3]{15 x b y})}{25 y^{2}}$

Step 8.1.2

Cancel the common factors.

Tap for more steps...

Step 8.1.2.1

Factor $5$ out of $25 y^{2}$ .

$\frac{5 (y \sqrt[3]{15 x b y})}{5 (5 y^{2})}$

Step 8.1.2.2

Cancel the common factor.

$\frac{5 (y \sqrt[3]{15 x b y})}{5 (5 y^{2})}$

Step 8.1.2.3

Rewrite the expression.

$\frac{y \sqrt[3]{15 x b y}}{5 y^{2}}$

Step 8.2

Cancel the common factor of $y$ and $y^{2}$ .

Tap for more steps...

Step 8.2.1

Factor $y$ out of $y \sqrt[3]{15 x b y}$ .

$\frac{y (\sqrt[3]{15 x b y})}{5 y^{2}}$

Step 8.2.2

Cancel the common factors.

Tap for more steps...

Step 8.2.2.1

Factor $y$ out of $5 y^{2}$ .

$\frac{y (\sqrt[3]{15 x b y})}{y (5 y)}$

Step 8.2.2.2

Cancel the common factor.

$\frac{y \sqrt[3]{15 x b y}}{y (5 y)}$

Step 8.2.2.3

Rewrite the expression.

$\frac{\sqrt[3]{15 x b y}}{5 y}$