Evaluate ( cube root of 2)÷( fourth root of 2)

$\sqrt[3]{2} \div \sqrt[4]{2}$

Rewrite the division as a fraction.

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

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

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

Combine and simplify the denominator.

Tap for more steps…

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

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

Raise $\sqrt[4]{2}$ to the power of $1$ .

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

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

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

Add $1$ and $3$ .

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

Rewrite ${\sqrt[4]{2}}^{4}$ as $2$ .

Tap for more steps…

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{2}$ as $2^{\frac{1}{4}}$ .

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

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

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

Combine $\frac{1}{4}$ and $4$ .

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

Cancel the common factor of $4$ .

Tap for more steps…

Cancel the common factor.

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

Divide $1$ by $1$ .

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

Evaluate the exponent.

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

Simplify the numerator.

Tap for more steps…

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

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

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

$\frac{\sqrt[3]{2} \sqrt[4]{8}}{2}$

Simplify the numerator.

Tap for more steps…

Rewrite the expression using the least common index of $12$ .

Tap for more steps…

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

$\frac{2^{\frac{1}{3}} \sqrt[4]{8}}{2}$

Rewrite $2^{\frac{1}{3}}$ as $2^{\frac{4}{12}}$ .

$\frac{2^{\frac{4}{12}} \sqrt[4]{8}}{2}$

Rewrite $2^{\frac{4}{12}}$ as $\sqrt[12]{2^{4}}$ .

$\frac{\sqrt[12]{2^{4}} \sqrt[4]{8}}{2}$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{8}$ as $8^{\frac{1}{4}}$ .

$\frac{\sqrt[12]{2^{4}} \cdot 8^{\frac{1}{4}}}{2}$

Rewrite $8^{\frac{1}{4}}$ as $8^{\frac{3}{12}}$ .

$\frac{\sqrt[12]{2^{4}} \cdot 8^{\frac{3}{12}}}{2}$

Rewrite $8^{\frac{3}{12}}$ as $\sqrt[12]{8^{3}}$ .

$\frac{\sqrt[12]{2^{4}} \sqrt[12]{8^{3}}}{2}$

Combine using the product rule for radicals.

$\frac{\sqrt[12]{2^{4} \cdot 8^{3}}}{2}$

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

$\frac{\sqrt[12]{2^{4} \cdot {(2^{3})}^{3}}}{2}$

Multiply the exponents in ${(2^{3})}^{3}$ .

Tap for more steps…

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

$\frac{\sqrt[12]{2^{4} \cdot 2^{3 \cdot 3}}}{2}$

Multiply $3$ by $3$ .

$\frac{\sqrt[12]{2^{4} \cdot 2^{9}}}{2}$

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

$\frac{\sqrt[12]{2^{4 + 9}}}{2}$

Add $4$ and $9$ .

$\frac{\sqrt[12]{2^{13}}}{2}$

Simplify the numerator.

Tap for more steps…

Raise $2$ to the power of $13$ .

$\frac{\sqrt[12]{8192}}{2}$

Rewrite $8192$ as $2^{12} \cdot 2$ .

Tap for more steps…

Factor $4096$ out of $8192$ .

$\frac{\sqrt[12]{4096 (2)}}{2}$

Rewrite $4096$ as $2^{12}$ .

$\frac{\sqrt[12]{2^{12} \cdot 2}}{2}$

Pull terms out from under the radical.

$\frac{2 \sqrt[12]{2}}{2}$

Cancel the common factor of $2$ .

Tap for more steps…

Cancel the common factor.

$\frac{2 \sqrt[12]{2}}{2}$

Divide $\sqrt[12]{2}$ by $1$ .

$\sqrt[12]{2}$

The result can be shown in multiple forms.

Exact Form:

$\sqrt[12]{2}$

Decimal Form:

$1.05946309 \dots$

Evaluate ( cube root of 2)÷( fourth root of 2)

Meet the Team our Math Expers

Our Professionals

Robert Kristofer

Anna Frok

Magnus Flores

Lydia Fran

We are MathExperts

We can solve all your math problems