1. The problem is to simplify the expression $16^{-\frac{3}{4}}$. 2. Recall the rule for negative exponents: $a^{-b} = \frac{1}{a^b}$. 3. Apply this rule to rewrite the expression: $$16^{-\frac{3}{4}} = \frac{1}{16^{\frac{3}{4}}}$$ 4. Next, express 16 as a power of 2 since 16 is $2^4$: $$\frac{1}{(2^4)^{\frac{3}{4}}}$$ 5. Use the power of a power rule: $(a^m)^n = a^{m \times n}$: $$\frac{1}{2^{4 \times \frac{3}{4}}} = \frac{1}{2^3}$$ 6. Simplify the exponent: $$\frac{1}{2^3} = \frac{1}{8}$$ 7. Therefore, the simplified value of $16^{-\frac{3}{4}}$ is $\frac{1}{8}$. This shows how to handle negative fractional exponents by converting to positive exponents and expressing the base in prime factors for easier simplification.