Simplify 4/( cube root of 4)

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

Step 1

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

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

Step 2

Combine and simplify the denominator.

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

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

Raise $\sqrt[3]{4}$ to the power of $1$ .

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

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

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

Add $1$ and $2$ .

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

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

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{4}$ as $4^{\frac{1}{3}}$ .

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

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

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Step 3

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide ${\sqrt[3]{4}}^{2}$ by $1$ .

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

Step 4

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

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

Step 5

Raise $4$ to the power of $2$ .

$\sqrt[3]{16}$

Step 6

Rewrite $16$ as $2^{3} \cdot 2$ .

Factor $8$ out of $16$ .

$\sqrt[3]{8 (2)}$

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

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

Step 7

Pull terms out from under the radical.

$2 \sqrt[3]{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt[3]{2}$

Decimal Form:

$2.51984209 \dots$

Simplify 4/( cube root of 4)

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