Simplify the Radical Expression (16/3)^(-3/4)

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

Step 1

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

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

Step 2

Apply the product rule to $\frac{3}{16}$ .

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

Step 3

Simplify the denominator.

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

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

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

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

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{3^{\frac{3}{4}}}{2^{3}}$

Raise $2$ to the power of $3$ .

$\frac{3^{\frac{3}{4}}}{8}$