The document contains a series of math problems involving powers and surds (irrational numbers) including: evaluating expressions with integer and fractional exponents; simplifying expressions with surds; rationalizing denominators containing surds; and expanding brackets containing surds. The problems cover topics such as evaluating expressions, simplifying surds, rationalizing denominators, and expanding brackets with surds.

1. Powers and Surds

2. What is the value of 2³

3. What is the value of 17 0

4. What is the value of 176283 1

5. 2 3 x2 11 =2 ?

6. 3 13 ÷3 9 =3 ?

8. What is 16 ½

10. What is 16 ¾

15. What is √3 x √3

16. What is √12 x √3

19. What is 3 √8 x 2 √2

22. Expand the brackets (2+ √3)(2- √3)

23. Expand the brackets (8 + 2√5)(4 - √5)