1. The problem asks to evaluate or simplify several mathematical expressions involving roots, powers, and fractions. 2. We will evaluate each expression step-by-step using the order of operations and properties of exponents and roots. 3. Expression 1: $\sqrt{4}$ - The square root of 4 is the number which when squared gives 4. - $\sqrt{4} = 2$ 4. Expression 2: $\frac{2}{5-3}$ - Simplify the denominator first: $5-3=2$ - So the expression becomes $\frac{2}{2}$ - Cancel common factors: $\frac{\cancel{2}}{\cancel{2}}=1$ 5. Expression 3: $3^2$ - This means 3 multiplied by itself: $3 \times 3 = 9$ 6. Expression 4: $\frac{\sqrt{3}}{8}$ - The numerator is $\sqrt{3}$, which is an irrational number approximately 1.732. - The denominator is 8. - The fraction remains as $\frac{\sqrt{3}}{8}$ or approximately 0.2165. 7. Expression 5: $\frac{13}{11}$ - This is a simple fraction, approximately 1.1818. 8. Expression 6: $\frac{17^8}{3^{13}}$ - Both numerator and denominator are powers. - We leave it as is or approximate: - $17^8 = 17^{8}$ (a very large number), $3^{13} = 1594323$ - Exact fraction: $\frac{17^8}{3^{13}}$ 9. Expression 7: $\frac{17}{8^3 - 11}$ - Calculate denominator: $8^3 = 512$ - So denominator: $512 - 11 = 501$ - Fraction: $\frac{17}{501}$ Final answers: - $\sqrt{4} = 2$ - $\frac{2}{5-3} = 1$ - $3^2 = 9$ - $\frac{\sqrt{3}}{8}$ (approx. 0.2165) - $\frac{13}{11}$ (approx. 1.1818) - $\frac{17^8}{3^{13}}$ - $\frac{17}{501}$