Evaluate (16/81)^(1/4)

${(\frac{16}{81})}^{\frac{1}{4}}$

Step 1

Apply the product rule to $\frac{16}{81}$ .

$\frac{16^{\frac{1}{4}}}{81^{\frac{1}{4}}}$

Step 2

Simplify the numerator.

Rewrite $16$ as $2^{4}$ .

$\frac{{(2^{4})}^{\frac{1}{4}}}{81^{\frac{1}{4}}}$

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

$\frac{2^{4 (\frac{1}{4})}}{81^{\frac{1}{4}}}$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{2^{4 (\frac{1}{4})}}{81^{\frac{1}{4}}}$

Rewrite the expression.

$\frac{2^{1}}{81^{\frac{1}{4}}}$

Evaluate the exponent.

$\frac{2}{81^{\frac{1}{4}}}$

Step 3

Simplify the denominator.

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

$\frac{2}{{(3^{4})}^{\frac{1}{4}}}$

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

$\frac{2}{3^{4 (\frac{1}{4})}}$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{2}{3^{4 (\frac{1}{4})}}$

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:

$0.\overline{6}$