Evaluate 1/(81^(1/4))

$\frac{1}{81^{\frac{1}{4}}}$

Step 1

Rewrite $81$ as $3^{4}$ .

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

Step 2

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

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

Step 3

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Evaluate the exponent.

$\frac{1}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{3}$

Decimal Form:

$0.\overline{3}$