Algebra Examples

$\frac{\sqrt[3]{5 z^{7} b^{4}}}{\sqrt[3]{25 x y}}$

Step 1

Combine $\sqrt[3]{5 z^{7} b^{4}}$ and $\sqrt[3]{25 x y}$ into a single radical.

$\sqrt[3]{\frac{5 z^{7} b^{4}}{25 x y}}$

Step 2

Reduce the expression $\frac{5 z^{7} b^{4}}{25 x y}$ by cancelling the common factors.

Tap for more steps...

Step 2.1

Factor $5$ out of $5 z^{7} b^{4}$ .

$\sqrt[3]{\frac{5 (z^{7} b^{4})}{25 x y}}$

Step 2.2

Factor $5$ out of $25 x y$ .

$\sqrt[3]{\frac{5 (z^{7} b^{4})}{5 (5 x y)}}$

Step 2.3

Cancel the common factor.

$\sqrt[3]{\frac{5 (z^{7} b^{4})}{5 (5 x y)}}$

Step 2.4

Rewrite the expression.

$\sqrt[3]{\frac{z^{7} b^{4}}{5 x y}}$

Step 3

Rewrite $\sqrt[3]{\frac{z^{7} b^{4}}{5 x y}}$ as $\frac{\sqrt[3]{z^{7} b^{4}}}{\sqrt[3]{5 x y}}$ .

$\frac{\sqrt[3]{z^{7} b^{4}}}{\sqrt[3]{5 x y}}$

Step 4

Simplify the numerator.

Tap for more steps...

Step 4.1

Rewrite $z^{7} b^{4}$ as ${(z^{2} b)}^{3} (z b)$ .

Tap for more steps...

Step 4.1.1

Factor out $z^{6}$ .

$\frac{\sqrt[3]{z^{6} z b^{4}}}{\sqrt[3]{5 x y}}$

Step 4.1.2

Rewrite $z^{6}$ as ${(z^{2})}^{3}$ .

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

Step 4.1.3

Factor out $b^{3}$ .

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

Step 4.1.4

Move $z$ .

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

Step 4.1.5

Rewrite ${(z^{2})}^{3} b^{3}$ as ${(z^{2} b)}^{3}$ .

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

Step 4.1.6

Add parentheses.

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

Step 4.2

Pull terms out from under the radical.

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

Step 5

Multiply $\frac{z^{2} b \sqrt[3]{z b}}{\sqrt[3]{5 x y}}$ by $\frac{{\sqrt[3]{5 x y}}^{2}}{{\sqrt[3]{5 x y}}^{2}}$ .

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

Step 6

Combine and simplify the denominator.

Tap for more steps...

Step 6.1

Multiply $\frac{z^{2} b \sqrt[3]{z b}}{\sqrt[3]{5 x y}}$ by $\frac{{\sqrt[3]{5 x y}}^{2}}{{\sqrt[3]{5 x y}}^{2}}$ .

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

Step 6.2

Raise $\sqrt[3]{5 x y}$ to the power of $1$ .

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

Step 6.3

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

$\frac{z^{2} b \sqrt[3]{z b} {\sqrt[3]{5 x y}}^{2}}{{\sqrt[3]{5 x y}}^{1 + 2}}$

Step 6.4

Add $1$ and $2$ .

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

Step 6.5

Rewrite ${\sqrt[3]{5 x y}}^{3}$ as $5 x y$ .

Tap for more steps...

Step 6.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{5 x y}$ as ${(5 x y)}^{\frac{1}{3}}$ .

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

Step 6.5.2

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

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

Step 6.5.3

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

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

Step 6.5.4

Cancel the common factor of $3$ .

Tap for more steps...

Step 6.5.4.1

Cancel the common factor.

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

Step 6.5.4.2

Rewrite the expression.

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

Step 6.5.5

Simplify.

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

Step 7

Simplify the numerator.

Tap for more steps...

Step 7.1

Rewrite ${\sqrt[3]{5 x y}}^{2}$ as $\sqrt[3]{{(5 x y)}^{2}}$ .

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

Step 7.2

Apply the product rule to $5 x y$ .

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

Step 7.3

Apply the product rule to $5 x$ .

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

Step 7.4

Raise $5$ to the power of $2$ .

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

Step 7.5

Combine using the product rule for radicals.

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