Evaluate (1/27)^(4/3)

${(\frac{1}{27})}^{\frac{4}{3}}$

Step 1

Simplify the expression.

Apply the product rule to $\frac{1}{27}$ .

$\frac{1^{\frac{4}{3}}}{27^{\frac{4}{3}}}$

One to any power is one.

$\frac{1}{27^{\frac{4}{3}}}$

Step 2

Simplify the denominator.

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

$\frac{1}{{(3^{3})}^{\frac{4}{3}}}$

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

$\frac{1}{3^{3 (\frac{4}{3})}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{1}{3^{3 (\frac{4}{3})}}$

Rewrite the expression.

$\frac{1}{3^{4}}$

Raise $3$ to the power of $4$ .

$\frac{1}{81}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{81}$

Decimal Form:

$0.01234567 \dots$