Simplify cube root of (81x^2y^3)/(8xy^4z)

$\sqrt[3]{\frac{81 x^{2} y^{3}}{8 x y^{4} z}}$

Reduce the expression $\frac{81 x^{2} y^{3}}{8 x y^{4} z}$ by cancelling the common factors.

Factor $x$ out of $81 x^{2} y^{3}$ .

$\sqrt[3]{\frac{x (81 x y^{3})}{8 x y^{4} z}}$

Factor $x$ out of $8 x y^{4} z$ .

$\sqrt[3]{\frac{x (81 x y^{3})}{x (8 y^{4} z)}}$

Cancel the common factor.

$\sqrt[3]{\frac{x (81 x y^{3})}{x (8 y^{4} z)}}$

Rewrite the expression.

$\sqrt[3]{\frac{81 x y^{3}}{8 y^{4} z}}$

Cancel the common factor of $y^{3}$ and $y^{4}$ .

Factor $y^{3}$ out of $81 x y^{3}$ .

$\sqrt[3]{\frac{y^{3} (81 x)}{8 y^{4} z}}$

Cancel the common factors.

Factor $y^{3}$ out of $8 y^{4} z$ .

$\sqrt[3]{\frac{y^{3} (81 x)}{y^{3} (8 y z)}}$

Cancel the common factor.

$\sqrt[3]{\frac{y^{3} (81 x)}{y^{3} (8 y z)}}$

Rewrite the expression.

$\sqrt[3]{\frac{81 x}{8 y z}}$

Rewrite $\frac{81 x}{8 y z}$ as ${(\frac{3}{2})}^{3} \frac{3 x}{y z}$ .

Factor the perfect power $3^{3}$ out of $81 x$ .

$\sqrt[3]{\frac{3^{3} \cdot (3 x)}{8 y z}}$

Factor the perfect power $2^{3}$ out of $8 y z$ .

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

Rearrange the fraction $\frac{3^{3} \cdot (3 x)}{2^{3} (y z)}$ .

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

Pull terms out from under the radical.

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

Rewrite $\sqrt[3]{\frac{3 x}{y z}}$ as $\frac{\sqrt[3]{3 x}}{\sqrt[3]{y z}}$ .

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

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

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

Combine fractions.

Combine and simplify the denominator.

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

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

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

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

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

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

Add $1$ and $2$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Combine.

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

Simplify the numerator.

Rewrite ${\sqrt[3]{y z}}^{2}$ as ${({(y z)}^{2})}^{\frac{1}{3}}$ .

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

Apply the product rule to $y z$ .

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

Combine using the product rule for radicals.

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

Move $3$ to the left of $y^{2} z^{2}$ .

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

Simplify cube root of (81x^2y^3)/(8xy^4z)

Related Questions

Support LCMGCF.com by disabling your adblocker.