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

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

Step 1

Change the sign of the exponent by rewriting the base as its reciprocal.

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

Step 2

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

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

Step 3

Simplify the numerator.

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

$\frac{{(3^{4})}^{\frac{1}{4}}}{16^{\frac{1}{4}}}$

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

$\frac{3^{4 (\frac{1}{4})}}{16^{\frac{1}{4}}}$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{3^{4 (\frac{1}{4})}}{16^{\frac{1}{4}}}$

Rewrite the expression.

$\frac{3^{1}}{16^{\frac{1}{4}}}$

Evaluate the exponent.

$\frac{3}{16^{\frac{1}{4}}}$

Step 4

Simplify the denominator.

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

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

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

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

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

$\frac{3}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{2}$

Decimal Form:

$1.5$

Mixed Number Form:

$1 \frac{1}{2}$