Evaluate cube root of 144/y

$\sqrt[3]{\frac{144}{y}}$

Step 1

Rewrite $\sqrt[3]{\frac{144}{y}}$ as $\frac{\sqrt[3]{144}}{\sqrt[3]{y}}$ .

$\frac{\sqrt[3]{144}}{\sqrt[3]{y}}$

Step 2

Simplify the numerator.

Rewrite $144$ as $2^{3} \cdot 18$ .

Factor $8$ out of $144$ .

$\frac{\sqrt[3]{8 (18)}}{\sqrt[3]{y}}$

Rewrite $8$ as $2^{3}$ .

$\frac{\sqrt[3]{2^{3} \cdot 18}}{\sqrt[3]{y}}$

Pull terms out from under the radical.

$\frac{2 \sqrt[3]{18}}{\sqrt[3]{y}}$

Step 3

Multiply $\frac{2 \sqrt[3]{18}}{\sqrt[3]{y}}$ by $\frac{{\sqrt[3]{y}}^{2}}{{\sqrt[3]{y}}^{2}}$ .

$\frac{2 \sqrt[3]{18}}{\sqrt[3]{y}} \cdot \frac{{\sqrt[3]{y}}^{2}}{{\sqrt[3]{y}}^{2}}$

Step 4

Combine and simplify the denominator.

Multiply $\frac{2 \sqrt[3]{18}}{\sqrt[3]{y}}$ by $\frac{{\sqrt[3]{y}}^{2}}{{\sqrt[3]{y}}^{2}}$ .

$\frac{2 \sqrt[3]{18} {\sqrt[3]{y}}^{2}}{\sqrt[3]{y} {\sqrt[3]{y}}^{2}}$

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

$\frac{2 \sqrt[3]{18} {\sqrt[3]{y}}^{2}}{{\sqrt[3]{y}}^{1} {\sqrt[3]{y}}^{2}}$

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

$\frac{2 \sqrt[3]{18} {\sqrt[3]{y}}^{2}}{{\sqrt[3]{y}}^{1 + 2}}$

Add $1$ and $2$ .

$\frac{2 \sqrt[3]{18} {\sqrt[3]{y}}^{2}}{{\sqrt[3]{y}}^{3}}$

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

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

$\frac{2 \sqrt[3]{18} {\sqrt[3]{y}}^{2}}{{(y^{\frac{1}{3}})}^{3}}$

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

$\frac{2 \sqrt[3]{18} {\sqrt[3]{y}}^{2}}{y^{\frac{1}{3} \cdot 3}}$

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

$\frac{2 \sqrt[3]{18} {\sqrt[3]{y}}^{2}}{y^{\frac{3}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{2 \sqrt[3]{18} {\sqrt[3]{y}}^{2}}{y^{\frac{3}{3}}}$

Rewrite the expression.

$\frac{2 \sqrt[3]{18} {\sqrt[3]{y}}^{2}}{y^{1}}$

Simplify.

$\frac{2 \sqrt[3]{18} {\sqrt[3]{y}}^{2}}{y}$

Step 5

Simplify the numerator.

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

$\frac{2 \sqrt[3]{18} \sqrt[3]{y^{2}}}{y}$

Combine using the product rule for radicals.

$\frac{2 \sqrt[3]{y^{2} \cdot 18}}{y}$

Step 6

Move $18$ to the left of $y^{2}$ .

$\frac{2 \sqrt[3]{18 y^{2}}}{y}$

Evaluate cube root of 144/y

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