Exponents and Radicals

1. Solve the below expression. (If it is a fraction, write it in m/n form)

(a)  

2. Assume that m is a negative integer and n is a positive integer. It is given that x = m, y = √n, z = n². Select all the options that must be correct from the below list of options

• z > y >x
• yz > x - y -z
• x > y >z
• y > x > z
• xy > x + y +z

• A
• B
• C
• D

4. Select all the alternate forms of √x / (x^2)

• 
• 
• 
• 
• 

5. A perfect cube is an integer whose cube root is an integer. For example, 27, 64 and 125 are perfect cubes. If m and n are perfect cubes, which of the following will not necessarily be a perfect cube?

• 8m
• mn
• mn + 216
• -m
• (m-n)⁹

6. If x ² > x ³ > x, which of the following must be true? I. x⁶ > x⁷ II. x can take any value between 0 and 1 III. -1 < x < 0

• Only I
• Only I and II
• Only III
• Both I and II
• Both I and III

7. It is given that x is a negative integer. Quantity A: x ⁷ + x ³ Quantity B: x⁸ + x⁶

• A
• B
• C
• D

8. It is given that x is an integer. Quantity A: x ⁷ + x ³ Quantity B: x⁸ + x⁶

• A
• B
• C
• D

9. Quantity A: The last digit of (1124 ^ 678) Quantity B: The last digit of (42 ^ 123)

• A
• B
• C
• D