Evaluate (1/243)^(1/5)

${(\frac{1}{243})}^{\frac{1}{5}}$

Step 1

Simplify the expression.

Apply the product rule to $\frac{1}{243}$ .

$\frac{1^{\frac{1}{5}}}{243^{\frac{1}{5}}}$

One to any power is one.

$\frac{1}{243^{\frac{1}{5}}}$

Step 2

Simplify the denominator.

Rewrite $243$ as $3^{5}$ .

$\frac{1}{{(3^{5})}^{\frac{1}{5}}}$

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

$\frac{1}{3^{5 (\frac{1}{5})}}$

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{1}{3^{5 (\frac{1}{5})}}$

Rewrite the expression.

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

Evaluate the exponent.

$\frac{1}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{3}$

Decimal Form:

$0.\overline{3}$