Evaluate cube root of (27(2)^4)/((3)^6)

$\sqrt[3]{\frac{27 {(2)}^{4}}{{(3)}^{6}}}$

Step 1

Simplify the expression.

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

$\sqrt[3]{\frac{27 \cdot 16}{3^{6}}}$

Raise $3$ to the power of $6$ .

$\sqrt[3]{\frac{27 \cdot 16}{729}}$

Multiply $27$ by $16$ .

$\sqrt[3]{\frac{432}{729}}$

Step 2

Cancel the common factor of $432$ and $729$ .

Factor $27$ out of $432$ .

$\sqrt[3]{\frac{27 (16)}{729}}$

Cancel the common factors.

Factor $27$ out of $729$ .

$\sqrt[3]{\frac{27 \cdot 16}{27 \cdot 27}}$

Cancel the common factor.

$\sqrt[3]{\frac{27 \cdot 16}{27 \cdot 27}}$

Rewrite the expression.

$\sqrt[3]{\frac{16}{27}}$

Step 3

Rewrite $\sqrt[3]{\frac{16}{27}}$ as $\frac{\sqrt[3]{16}}{\sqrt[3]{27}}$ .

$\frac{\sqrt[3]{16}}{\sqrt[3]{27}}$

Step 4

Simplify the numerator.

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

Factor $8$ out of $16$ .

$\frac{\sqrt[3]{8 (2)}}{\sqrt[3]{27}}$

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

$\frac{\sqrt[3]{2^{3} \cdot 2}}{\sqrt[3]{27}}$

Pull terms out from under the radical.

$\frac{2 \sqrt[3]{2}}{\sqrt[3]{27}}$

Step 5

Simplify the denominator.

Rewrite $27$ as $3^{3}$ .

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

Pull terms out from under the radical, assuming real numbers.

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.83994736 \dots$