Simplify ( cube root of 8)÷( cube root of 6)

$\sqrt[3]{8} \div \sqrt[3]{6}$

Step 1

Rewrite the division as a fraction.

$\frac{\sqrt[3]{8}}{\sqrt[3]{6}}$

Step 2

Combine $\sqrt[3]{8}$ and $\sqrt[3]{6}$ into a single radical.

$\sqrt[3]{\frac{8}{6}}$

Step 3

Cancel the common factor of $8$ and $6$ .

Factor $2$ out of $8$ .

$\sqrt[3]{\frac{2 (4)}{6}}$

Cancel the common factors.

Factor $2$ out of $6$ .

$\sqrt[3]{\frac{2 \cdot 4}{2 \cdot 3}}$

Cancel the common factor.

$\sqrt[3]{\frac{2 \cdot 4}{2 \cdot 3}}$

Rewrite the expression.

$\sqrt[3]{\frac{4}{3}}$

Step 4

Rewrite $\sqrt[3]{\frac{4}{3}}$ as $\frac{\sqrt[3]{4}}{\sqrt[3]{3}}$ .

$\frac{\sqrt[3]{4}}{\sqrt[3]{3}}$

Step 5

Multiply $\frac{\sqrt[3]{4}}{\sqrt[3]{3}}$ by $\frac{{\sqrt[3]{3}}^{2}}{{\sqrt[3]{3}}^{2}}$ .

$\frac{\sqrt[3]{4}}{\sqrt[3]{3}} \cdot \frac{{\sqrt[3]{3}}^{2}}{{\sqrt[3]{3}}^{2}}$

Step 6

Combine and simplify the denominator.

Multiply $\frac{\sqrt[3]{4}}{\sqrt[3]{3}}$ by $\frac{{\sqrt[3]{3}}^{2}}{{\sqrt[3]{3}}^{2}}$ .

$\frac{\sqrt[3]{4} {\sqrt[3]{3}}^{2}}{\sqrt[3]{3} {\sqrt[3]{3}}^{2}}$

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

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

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

$\frac{\sqrt[3]{4} {\sqrt[3]{3}}^{2}}{{\sqrt[3]{3}}^{1 + 2}}$

Add $1$ and $2$ .

$\frac{\sqrt[3]{4} {\sqrt[3]{3}}^{2}}{{\sqrt[3]{3}}^{3}}$

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

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

$\frac{\sqrt[3]{4} {\sqrt[3]{3}}^{2}}{{(3^{\frac{1}{3}})}^{3}}$

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

$\frac{\sqrt[3]{4} {\sqrt[3]{3}}^{2}}{3^{\frac{1}{3} \cdot 3}}$

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

$\frac{\sqrt[3]{4} {\sqrt[3]{3}}^{2}}{3^{\frac{3}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{\sqrt[3]{4} {\sqrt[3]{3}}^{2}}{3^{\frac{3}{3}}}$

Rewrite the expression.

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

Evaluate the exponent.

$\frac{\sqrt[3]{4} {\sqrt[3]{3}}^{2}}{3}$

Step 7

Simplify the numerator.

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

$\frac{\sqrt[3]{4} \sqrt[3]{3^{2}}}{3}$

Raise $3$ to the power of $2$ .

$\frac{\sqrt[3]{4} \sqrt[3]{9}}{3}$

Step 8

Simplify the numerator.

Combine using the product rule for radicals.

$\frac{\sqrt[3]{4 \cdot 9}}{3}$

Multiply $4$ by $9$ .

$\frac{\sqrt[3]{36}}{3}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt[3]{36}}{3}$

Decimal Form:

$1.10064241 \dots$

Simplify ( cube root of 8)÷( cube root of 6)

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