Practice and Problem-Solving Exercises

A Practice

See Problems 1 and 2.

Simplify each expression.

9. 3 5 3 to the fifth
10. 4 3 4 cubed
11. 2 4 2 to the fourth
12. 10 8 10 to the eighth
13. ( 2 3 ) 3 open , 2 thirds , close cubed
14. ( 1 2 ) 4 open , 1 half , close to the fourth
15. ( 0.4 ) 6 open 0.4 close to the sixth
16. 7 4 7 to the fourth
17. 20 − 2 · 3 2 20 minus 2 middle dot , 3 squared
18. 6 + 4 ÷ 2 + 3 6 plus 4 divides 2 plus 3
19. ( 6 2 − 3 3 ) ÷ 2 open , 6 squared , minus , 3 cubed , close divides 2
20. 5 · 2 2 ÷ 2 + 8 5 middle dot , 2 squared , divides 2 plus 8
21. 80 − ( 4 − 1 ) 3 80 minus . open 4 minus 1 close cubed
22. 52 + 8 2 − 3 ( 4 − 2 ) 3 52 plus , 8 squared , minus 3 . open 4 minus 2 close cubed
23. 6 4 ÷ 3 2 9 fraction 6 to the fourth , divides , 3 squared , over 9 end fraction
24. 2 ⋅ 7 + 4 9 ÷ 3 fraction 2 dot 7 plus 4 , over 9 divides 3 end fraction

See Problem 3.

Evaluate each expression for s = 4 bold italic s equals 4  and t = 8 . bold italic t equals 8 .

25. ( s + t ) 3 open s plus t close cubed
26. s 4 + t 2 + s ÷ 2 s to the fourth , plus , t squared , plus s divides 2
27. ( s t ) 2 open s t close squared
28. 3 s t 2 ÷ ( s t ) + 6 3 s , t squared , divides open s t close plus 6
29. ( t − s ) 5 open t minus s close to the fifth
30. ( 2 s ) 2 t open 2 s close squared . t
31. 2 s t 2 − s 2 2 s , t squared , minus , s squared
32. 2 s 2 − t 3 ÷ 16 2 , s squared , minus , t cubed , divides 16

33. ( 3 s ) 3 t + t s fraction open , 3 s , close cubed . t plus t , over s end fraction

See Problem 4.

34. Write an expression for the amount of change you will get when you pay for a purchase p with a $20 bill. Make a table to find the amounts of change you will get for purchases of $11.59, $17.50, $19.00, and $20.00.
35. An object's momentum is defined as the product of its mass m and velocity v. Write an expression for the momentum of an object. Make a table to find the momentums of a vehicle with a mass of 1000 kg moving at a velocity of 15 m/s, 20 m/s, and 25 m/s.

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