Exponents And Radicals — Important Questions

1/9

Step 1: We need to find 3^(-2) using the negative exponent law. Step 2: The law states that a^(-n) = 1/a^n for any non-zero number a. Step 3: Apply this law: 3^(-2) = 1/3^2. Step 4: Calculate 3^2 = 3 × 3 = 9. Step 5: Therefore, 3^(-2) = 1/9.

2^6

Step 1: We need to simplify (2^3)^2 using the power of a power law. Step 2: The law states that (a^m)^n = a^(mn). Step 3: Here, a = 2, m = 3, and n = 2. Step 4: Apply the law: (2^3)^2 = 2^(3×2) = 2^6. Step 5: Therefore, (2^3)^2 = 2^6.

4

Step 1: We need to find √16, which means finding a number that when squared gives 16. Step 2: We need to find x such that x^2 = 16. Step 3: Check: 4^2 = 4 × 4 = 16. Step 4: Since 4^2 = 16, we have √16 = 4. Step 5: Therefore, √16 = 4.

4

Step 1: We use the law √a × √b = √(ab) to multiply the radicals. Step 2: Apply the law: √2 × √8 = √(2 × 8) = √16. Step 3: Calculate the value under the radical: 2 × 8 = 16. Step 4: Find √16 = 4 (since 4^2 = 16). Step 5: Therefore, √2 × √8 = 4.