Simplify 8/( cube root of 16)

$\frac{8}{\sqrt[3]{16}}$

Step 1

Simplify the denominator.

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

Factor $8$ out of $16$ .

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

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

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

Pull terms out from under the radical.

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

Step 2

Cancel the common factor of $8$ and $2$ .

Factor $2$ out of $8$ .

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

Cancel the common factors.

Factor $2$ out of $2 \sqrt[3]{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

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

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

Step 4

Combine and simplify the denominator.

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

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

Raise $\sqrt[3]{2}$ to the power of $1$ .

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

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

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

Add $1$ and $2$ .

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

Rewrite ${\sqrt[3]{2}}^{3}$ as $2$ .

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

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

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

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Step 5

Cancel the common factor of $4$ and $2$ .

Factor $2$ out of $4 {\sqrt[3]{2}}^{2}$ .

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

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Step 6

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

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

Step 7

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

$2 \sqrt[3]{4}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt[3]{4}$

Decimal Form:

$3.17480210 \dots$

Simplify 8/( cube root of 16)

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