Simplify the Radical Expression (112/7)^(-1/4)

${(\frac{112}{7})}^{- \frac{1}{4}}$

Divide $112$ by $7$ .

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

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Simplify the denominator.

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

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

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

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

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

$\frac{1}{2}$