1. **State the problem:** Calculate $\frac{3}{4}$ of $5^{-\frac{1}{2}}$. 2. **Recall the rules:** - A negative exponent means the reciprocal: $a^{-n} = \frac{1}{a^n}$. - Fractional exponents mean roots: $a^{\frac{1}{2}} = \sqrt{a}$. 3. **Rewrite the expression:** $$\frac{3}{4} \times 5^{-\frac{1}{2}} = \frac{3}{4} \times \frac{1}{5^{\frac{1}{2}}} = \frac{3}{4} \times \frac{1}{\sqrt{5}}$$ 4. **Multiply the fractions:** $$\frac{3}{4} \times \frac{1}{\sqrt{5}} = \frac{3}{4\sqrt{5}}$$ 5. **Rationalize the denominator:** Multiply numerator and denominator by $\sqrt{5}$: $$\frac{3}{4\sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}} = \frac{3\sqrt{5}}{4 \times 5} = \frac{3\sqrt{5}}{20}$$ **Final answer:** $$\frac{3\sqrt{5}}{20}$$