1. Problem: Calculate $29 \times 3^2$. Step 1: Calculate the exponent: $3^2 = 9$. Step 2: Multiply: $29 \times 9 = 261$. 2. Problem: Calculate $(2.7)^2 \times 3^2$. Step 1: Calculate each exponent: $(2.7)^2 = 7.29$, $3^2 = 9$. Step 2: Multiply: $7.29 \times 9 = 65.61$. 3. Problem: Calculate $27^{1/3}$ (cube root of 27). Step 1: $27^{1/3} = 3$ because $3^3 = 27$. 4. Problem: Calculate $\sqrt[3]{12^6}$. Step 1: Express as $(12^6)^{1/3} = 12^{6 \times \frac{1}{3}} = 12^2$. Step 2: Calculate $12^2 = 144$. 5. Problem: Calculate $2^{-1/2}$. Step 1: $2^{-1/2} = \frac{1}{2^{1/2}} = \frac{1}{\sqrt{2}}$. 6. Problem: Calculate $9^{1/2}$. Step 1: $9^{1/2} = \sqrt{9} = 3$. 7. Problem: Calculate $(25q^2)^{1/2}$. Step 1: Apply the exponent to each factor: $25^{1/2} q^{2 \times 1/2} = 5q$. 8. Problem: Calculate $(2.9)^{-1}$. Step 1: $ (2.9)^{-1} = \frac{1}{2.9} \approx 0.3448$. 9. Problem: Calculate $2^{-2} \times 2^3$. Step 1: Use laws of exponents: $2^{-2 + 3} = 2^1 = 2$. 10. Problem: Calculate $\frac{10^{-2}}{4}$. Step 1: Calculate numerator: $10^{-2} = 0.01$. Step 2: Divide by 4: $\frac{0.01}{4} = 0.0025$. 11. Problem: Simplify $3q$ (no calculation needed). Step 1: Expression remains $3q$. 12. Problem: Calculate $5\sqrt{3^4}$. Step 1: Calculate $3^4 = 81$. Step 2: Calculate $\sqrt{81} = 9$. Step 3: Multiply by 5: $5 \times 9 = 45$. 13. Problem: Calculate $7^{-1}$. Step 1: $7^{-1} = \frac{1}{7}$. 14. Problem: Calculate $3^2 \times 3^{3/2}$. Step 1: Sum exponents: $2 + \frac{3}{2} = \frac{4}{2} + \frac{3}{2} = \frac{7}{2}$. Step 2: Result: $3^{7/2}$. 15. Problem: Calculate $3^2 \times 3^{-3/2}$. Step 1: Sum exponents: $2 - \frac{3}{2} = \frac{4}{2} - \frac{3}{2} = \frac{1}{2}$. Step 2: Result: $3^{1/2} = \sqrt{3}$. 16. Problem: Calculate $2^9 \times (3q)^2$. Step 1: Calculate $2^9 = 512$. Step 2: Expand $(3q)^2 = 3^2 q^2 = 9 q^2$. Step 3: Multiply: $512 \times 9 q^2 = 4608 q^2$. 17. Problem: Expression given as $2^9 \times 3^2 -$ which seems incomplete. Step 1: Calculate what is given: $2^9 = 512$, $3^2 = 9$. Step 2: Multiply: $512 \times 9 = 4608$. Step 3: Since expression incomplete, result is $4608 - $ (needs more data). 18. Problem: Calculate $2^{1/2} \times 2^{3/2}$. Step 1: Sum exponents: $\frac{1}{2} + \frac{3}{2} = 2$. Step 2: Result: $2^2 = 4$. 19. Problem: Calculate $12.5^{-2/3}$. Step 1: $12.5^{-2/3} = \frac{1}{12.5^{2/3}}$. Step 2: Calculate cube root: $12.5^{1/3} \approx 2.35$. Step 3: Square it: $(2.35)^2 \approx 5.52$. Step 4: Inverse: $\frac{1}{5.52} \approx 0.181$. 20. Problem: Calculate $16^{-2/4}$. Step 1: Simplify exponent: $-2/4 = -0.5$. Step 2: Calculate $16^{-0.5} = \frac{1}{\sqrt{16}} = \frac{1}{4} = 0.25$. 21. Problem: Calculate $29 \times 39^2$. Step 1: Calculate $39^2 = 1521$. Step 2: Multiply: $29 \times 1521 = 44,109$. 22. Problem: Calculate $4^{-3/2}$. Step 1: Express as $\frac{1}{4^{3/2}}$. Step 2: Calculate $4^{3/2} = (\sqrt{4})^3 = 2^3 = 8$. Step 3: Result: $\frac{1}{8} = 0.125$. Final answers: 1) 261 2) 65.61 3) 3 4) 144 5) $\frac{1}{\sqrt{2}}$ 6) 3 7) $5q$ 8) $\approx 0.3448$ 9) 2 10) 0.0025 11) $3q$ 12) 45 13) $\frac{1}{7}$ 14) $3^{7/2}$ 15) $\sqrt{3}$ 16) $4608 q^2$ 17) Incomplete 18) 4 19) $\approx 0.181$ 20) 0.25 21) 44109 22) 0.125