Evaluate (8/27)^(1/3)

${(\frac{8}{27})}^{\frac{1}{3}}$

Step 1

Apply the product rule to $\frac{8}{27}$ .

$\frac{8^{\frac{1}{3}}}{27^{\frac{1}{3}}}$

Step 2

Simplify the numerator.

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

$\frac{{(2^{3})}^{\frac{1}{3}}}{27^{\frac{1}{3}}}$

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

$\frac{2^{3 (\frac{1}{3})}}{27^{\frac{1}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{2^{3 (\frac{1}{3})}}{27^{\frac{1}{3}}}$

Rewrite the expression.

$\frac{2^{1}}{27^{\frac{1}{3}}}$

Evaluate the exponent.

$\frac{2}{27^{\frac{1}{3}}}$

Step 3

Simplify the denominator.

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

$\frac{2}{{(3^{3})}^{\frac{1}{3}}}$

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

$\frac{2}{3^{3 (\frac{1}{3})}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{2}{3^{3 (\frac{1}{3})}}$

Rewrite the expression.

$\frac{2}{3^{1}}$

Evaluate the exponent.

$\frac{2}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{3}$

Decimal Form:

$0.\overline{6}$